IAL 31: Cosmology

Don't Panic

Sections

1. Introduction
2. Cosmology, Human Concerns, and Philosophy
3. The Early History of Cosmology
4. The Expansion of the Universe
5. Cosmological Distance Measures Explained
6. Einstein, General Relativity, and the Einstein Universe
7. Friedmann-Lemaitre Models
8. The Accelerating Universe and the Friedmann-Lemaitre-Lambda Models
9. Dark Energy
10. The Concordance Model
11. The Fate of the Universe According to the Concordance Model
12. Big Bang Cosmology and the Constituents of Observable Universe
13. Inflation and Inflation Cosmology
14. Conclusion

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Introduction

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Physical cosmology---which hereafter we usually just call cosmology--- is the science of the universe as a whole.

But, of course, it is not the science of everything.

Cosmology restricts itself to average behavior of the universe and, at just a smaller scale, to the large-scale structure of the universe: galaxies, galaxy clusters, superclusters of galaxies, galaxy filaments, sheets, and voids.

But to study cosmology entails understanding smaller things than the universe and the large-scale structure of the universe to some degree: e.g., understanding stars, supernovae, super massive black holes, quasars, atoms, molecules, atomic nuclei, and quarks.

The understanding of the smaller things is only needed insofar as it affects the big things.

The physics needed for cosmology is first of all general relativity.

General relativity is out best theory of gravity and motion under gravity.

It is gravity that determines the motion of the universe as a whole and the evolution of the large-scale structure.

Newtonian gravity was shown to be inadequate for cosmology as we will discuss below in the section The Early History of Cosmology. So the more general theory, general relativity, is needed. General relativity is our best theory of gravity so far. It will may be supplanted as that by a theory of quantum gravity some day.

We briefly covered the large-scale structure in IAL 28: Galaxies: Clusters, Superclusters, and Large-Scale Structure.

We will NOT add to that discussion in this lecture.

But cosmology also requires classical physics (including thermodynamics), quantum mechanics, and quantum field theory (which is relativistic quantum mechanics).

There are many things which are definitely excluded from cosmology: e.g., planets, biology, humans, psychology, the Oedipus complex, etc.

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Cosmology, Human Concerns, and Philosophy

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Cosmology in the broad sense has always been of importance to humankind.

We are concerned about the meaning, purpose, and nature of our own existence.

Therefore about the meaning, purpose, and nature of the universe which sustains us and everything else.

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Caption: "Melancholia I, 1514.

The angel of melancholy among her scattered instruments and experiments---contemplating existence on supposes.

Credit/Permission: Albrecht Duerer (1471--1528), 1514 / Public domain.

Image linked to Wikipedia.

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Modern physical cosmology of course, concerns itself with NATURE OF and leaves aside MEANING AND PURPOSE.

But MEANING AND PURPOSE probably hover just somewhere beyond the expressed concerns of many modern scientific cosmologists and are probably of interest to everyone interested in cosmology.

Cosmology and extraterrestrial life are the two fields of modern astronomy that are of most interest to general public and to astronomers themselves.

It seems overwhelmingly likely because of their strong connection to MEANING AND PURPOSE of our own existence.

As The Hitchhiker's Guide to the Galaxy put it: the answer to the ultimate question of life, the universe, and everything.

The answer being 42---which was sort of an let-down.

If we ever did finally fathom the universe, it is easy to believe that that knowledge would have PHILOSOPHICAL IMPLICATIONS.

But modern scientific cosmologists are usually---but not always---reluctant to connect current thinking with philosophical theories.

They are well aware that modern cosmological theories may well be WRONG or SUPERFICIAL, and so drawing philosophical conclusions is premature---and, of course, we are not sure know how to draw them accurately anyway.

Of course, it is possible to draw correct conclusions from a wrong theory, but that's not very likely.

One can go the other way and try to derive or constrain cosmology from philosophical ideas. Using philosophical ideas as source of heuristic cosmological hypotheses has been done. This is valid in the scientific method as long as the philosophical ideas are NOT taken as dogma.

For an example of a reluctant cosmologist, consider Georges Lemaitre (1894--1966). He can be justly considered the grandparent of the Big Bang theory was a Roman Catholic priest et devote a la foi, naturalmente (No-525,530).

But Lemaitre resisted identification of his primeval atom (the theoretical ancestor of the Big Bang theory) with the creation of Genesis.

The former was speculative science; the latter, faith.

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Caption: Georges Lemaitre (1894--1966).

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Caption: Georges Lemaitre (1894--1966) circa 1933.

Lemaitre was the co-discoverer of the Friedmann-Lemaitre models and the inventor of the primeval atom in 1931 which is the ancestor of the Big Bang theory. The primeval atom is now only of historical interest.

He is sort of the grandparent of the Big Bang theory.

Credit: Unknown photographer, circa 1933 (Uploaded to Wikipedia by User:Maksim, Public domain.

Image linked to Wikipedia.

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Caption: Georges Lemaitre (1894--1966) with Robert Millikan (1868--1953) and Albert Einstein (1879--1955) at Caltech, 1933 Jan10.

Some vandal folded and creased this historic photograph.

The vandal also forgot to scribble Lemaitre name on his legs---which will ultimately lead to him being described as "unknown".

Credit/Permission: Unknown photographer / The image is probably public domain. since it is from 1933jan10 and is probably out of copyright. You will have to click on cartoon to see the image.

Image linked to Centre de recherche sur la Terre et le climat Georges Lemaitre: Georges Lemaitre historical site.

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We will argue below the Big Bang theory is NOT just speculative science anymore: it is probably essentially right as far as it goes: at least it would be astonishing if it were just WRONG. (See the section Big Bang Cosmology and the Constituents of Observable Universe.)

But Big Bang theory doesn't in itself tell us what happened before the Big Bang, what happened in other universe domains if they exist, and what the fate of the universe or our universe domain will be.

Thus, Big Bang theory is actually superficial---despite the fact that it explains an awful lot about space and time.

Universe domain---say what?

In modern cosmology (most notably in inflation cosmology which we discuss below in section Inflation and Inflation Cosmology), it is possible that the universe of known structure (which consists of observable universe and some unobservable surroundings) may be part of a larger universe of different structure.

This larger universe has been called the multiverse.

This creates a bit of a quandary of terminology.

Do we refer to the multiverse and the perhaps, an uncountable infinity of universes?

Or do we refer to the universe as everything physical and to universe domains as regions of particular physical law?

The former violates our ordinary meaning of the universe as everything phyiscal?

The latter causes us to take a speculative theory as basis for a lot of jargon.

I've decided to flip back and forth---but not consistently.

"Do I contradict myself? Very well, then I contradict myself, I am large, I contain multitudes."

            Walt Whitman (1819--1892). See Walt Whitman Quotes.

Context must decide what is meant---but that's often the case.
Your truly will probably end up accepting the multiverse and multiple universes jargon eventually.

By the way, universe domain is not a standard term.

Instead of universe domain, some say pocket universe, bubble universe, or just universe.

The other universe domains may have different physical law from ours.

But not all physical law. A usual assumption is that only low-energy physical law is different. Low-energy in this context means anything less than a extremely relativistic motions.

In any case, folks believe that the concepts of energy and and thermodynamics apply in other universe domains

Unless at least some known physical law applied everywhere, we would be without any guidance and would have to admit knowing nothing about other universe domains---maybe we do know nothing.

Universe domains illustrated.

Where are the other universe domains?

Cosmologists often do a good job of not saying.

But one view is that that they are geometrically connected but we can't reach them since our universe domain and the space between universe domains is expanding too quickly (Alexander Vilenkin & Max Tegmark, 2011, Scientific American, The Case for Parallel Universes.)

Another view is that they are geometrically detached. The universe domains could be like hyperspheres: a finite, but unbounded spaces.

We discuss hyperspheres below in section Einstein, General Relativity, and the Einstein Universe.

Resuming after the digression, Big Bang cosmology is superficial in the deepest sense---or so most cosmologists would say, I think.

The issues outside of Big Bang cosmology are dealt with in broader theories, but those theories are more speculative and may well be just WRONG.

Currently, only two broader theories have much of a vogue: inflation cosmology (very much the frontrunner) and the ekpyrotic universe (very much the hindmost).

We will discuss inflation cosmology and, briefly, the ekpyrotic universe below in the section Inflation and Inflation Cosmology.

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In the past, cosmologists have NOT been so circumspect about the PHILOSOPHICAL IMPLICATIONS of physical cosmology.

Myth-oriented cosmologists and philosophical cosmologists were or are often concerned with these implications.

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Caption: Detail of "The School of Athens" (1509) by Raphael (1483--1520) showing Plato (428/427--348/347 BCE) on the left and Aristotle (384--322 BCE) on the right.

The possibly involuntary model for Plato may have been Leonardo da Vinci (1452--1519).

Credit/Permission: Raphael (1483--1520), 1509 (uploaded to Wikipedia by User:Jacobolus, 2005) / Public domain.

Image linked to Wikipedia.

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Certainly, it's fun to play in philosophy provided you don't take your own idiosyncratic ideas too seriously.

And who's to say when the next great advance in understanding in philosophy will come and clarify things for us.

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The Early History of Cosmology

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All early human societies, one supposes, had their own cosmological stories.

Most of these, one supposes---one hasn't done an actual count---have anthropomorphic dieties that order the universe.

But in even in these myths there is one supposes---one hasn't done an actual count---a regression to some simple early state with very primitive matter and a very primitive order perhaps somewhat personified as a very primitive god.

For example, the ancient Greek Hesiod's (circa late 8th century BCE) Theogony (origin of the gods: see Hesiod's Theogony translated by Hugh G. Evelyn-White 1914) posits Chaos as the first god and next Gaia (Mother Earth) and then other useful gods: Uranus (Sky), Tartaros (Hell), Eros (Love), Erebos (Gloom), Nyx (Night), etc. (see The Structure of Hesiod's Theogony: Joe Farrell, University of Pennsylvania).

These earlier primordial gods don't have much personality and are not really distinguishable from places, substances, or forces depending on their nature.

Gods with more personality come in later generations.

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Caption: The Pseudo-Seneca is an ancient Roman bronze (late 1st century BCE) at the Naples National Archaeological Museum, Naples, Italy. The bust was originally thought to be of Seneca (c. 4 BCE--65 CE). But nowadays it is considered to be possibly an imagined portrait of Hesiod (circa late 8th century BCE) or Aristophanes (c. 446--c. 386 BCE).

Hesiod is the author of the long poems Theogony and Works and Days.

Hesiod as revealed in Works and Days---which may not be by Hesiod, but by another Greek of the same name---is a rather gloomy, pessimistic farmer-poet---maybe a lot like Robert Frost (1874--1963)---the bust artist may have been trying to capture that character.

Credit/Permission: © Massimo Finizio (AKA User:Finizio), 2005 / Creative Commons CC BY-SA 2.0.

Image linked to Wikipedia.

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Hesiod (circa late 8th century BCE) videos:
1. Hesiod's Theogony - Greek Creation - Part 1 Too long for the classroom.
2. Ancient Greek: Reconstructed Pronunciation: Hesiod But is it in a Boeotian accent? Too long for the classroom.
3. Fiction Book Review: Hesiod and Theognis (Penguin Classics): Theogony, Works and Days, and Elegie... A brief intro to the translations by Dorothea Wender (1935--2003). Apparently, "Hesiod" is pronounce He-zide. See also Forvo: Hesiod, where it's He-siod. But who really knows---maybe it was Hayseed. Too long for the classroom.

Mythological cosmology videos:
1. Greek Mythology- The creation Probably based mostly on Hesiod's (circa late 8th century BCE) Theogony (origin of the gods). Too long for the classroom.
2. Norse Mythology 1 Creation of the Universe The origins in Norse mythology. Too long for the classroom.

So it seems that humankind are predisposed to think that there must be a relatively simple beginning in time---or more abstractly outside of time---as Boethius (ca. 480--524 or 525) thought.

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Caption: "Boethius (ca. 480--524 or 525): Consolation of philosophy. This early printed book has many hand-painted illustrations depicting Lady Philosophy and scenes of daily life in 15th-century Ghent (1485)."

Credit: Unknown Dutch artist of the 15th century, 1485 / Public domain.

Image linked to Wikipedia.

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The ancient Greek Pre-Socratic philosophers beginning in the 6th century BCE are the first persons recorded in history to try to develop philosophical theories about the universe---by philosophical theories, your truly means those subject to argument, empirical investagition, and correction.

The Pre-Socratics were---compared to modern standards---weak on detailed observation and experimentation---they did practise them at least a little at times---and this weakness limited their progress in cosmology and all other sciences as well. They relied on casual observations and reasoning and argument. Their understanding of what we call the scientific method was poor.

One can characterize much of the theorizing of the Pre-Socratic philosophers as the making of RATIONAL MYTHS.

Some of their theories are very interesting.

The cosmology of the Greek atomist philosophers Leucippus (first half of 5th century BCE) and Democritus (c. 460--c. 370 BCE) posited infinitely many worlds forming in vortices out of an infinite space of atoms in motion.

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Caption: "Democritus (ca. 460--ca. 370 BCE) meditating on the seat of the soul (1868) by Leon-Alexandre Delhomme (1841--1893 or 1895)."

Democritus was foremost exponent of atomism among the ancient Greeks.

Credit/Permission: © User:Jean-Louis Lascoux / Creative Commons CC BY-SA 3.0.

Image linked to Wikipedia.

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Democritus (ca. 460--ca. 370 BCE) videos:
1. Carl Sagan - Cosmos - Democritus Too long for the classroom.
2. Democritus And Atomic Theory A bit dull. Too long for the classroom.

We have only fragmentary information about the atomist cosmology from later source. No complete works by the Greek atomists survive.

However, the idea of VORTEX WORLDS seems to have been that a region atoms in the infinite universe (το παν = to pan = the all) would spontaneously or otherwise go into a swirling motion that would form an outer menbrane that was probably spherical.

The membrane was the outer edge of a VORTEX WORLD.

The membrane of our VORTEX WORLD seems to be essentially the celestial sphere of the stars.

The universe may have had no up and down, but a VORTEX WORLD did or at least ours did. At the bottom of our VORTEX WORLD there was residue of atoms that formed the flat Earth.

The universe and the atoms were eternal, but the VORTEX WORLDS were always being generated and destroyed. Our VORTEX WORLD at least had a long lifetime in comparison to human lifetime.

A VORTEX WORLD was a COSMOS---a word meaning something like ornamented thing.

Popular opinion is correct: cosmology and cosmetology are the same thing.

The idea of VORTEX WORLDS was certainly suggested by the daily rotation of the celestial sphere.

The following long-exposure image makes Democritus's thinking palpable.

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Gemini North is an 8-meter telescope on Mauna Kea, Hawaii.

Mauna Kea peaks at 4,145 m (13,600 ft) and is one of the world's best observing sites---located fortunately in one of the world's best tourist sites---still the air is thin up on the mountain.

Here we see a swirl of stars in a long-exposure image.

The star trails seem to be about 30 degrees (1/12 of 360 degrees), and so the exposure was about 2 hours (1/12 of a day).

Credit/Permission: Gemini Observatory /NOAO /AURA/NSF, © NOAO/AURA / NOAO/AURA Image Library Conditions of Use.

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Democritus (c. 460--c. 370 BCE) didn't have long exposure images, but he could watch the sky swirl around any clear night---an in pre-industrial times, people were much more conscious of the behavior of the sky and could see it better without light pollution

The idea that the Earth was at the bottom of giant vortex---that was tilted so that the axis wasn't at Zenith---could seem plausible.

Of course, Democritus should have clued into the spherical Earth theory that was already well known in his day.

The VORTEX WORLD membrane was ruled by the Copernican revolution.

Whimsically, one might take spiral galaxies as the modern analogs to the VORTEX WORLDS.

But, of course, Democritus's knew nothing of the spiral nebulae.

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Caption: "This is the sketch made by Lord Rosse of the Whirlpool Galaxy in 1845."

The Whirlpool Galaxy (AKA M51) is in Canes Venatici (the Hunting Dogs).

The Whirlpool Galaxy is actually two galaxies: NGC 5194/M51a (Sc), a large Sc spiral and a smaller companion NGC 5195/M51b (SB?) which a sort of barred spiral galaxy.

The Whirlpool Galaxy is about 8.5 Mpc away and 20 kpc across.

The spiral nature of some galaxies (historically spiral nebulae) was first discovered from Whirlpool Galaxy by William Parsons, 3rd Earl of Rosse (1800-1867) in 1845apr at Birr Castle, Parsontown, Ireland using the Leviathan of Parsonstown (a 1.83 m diameter telescope) (CK-366; No-435--437).

Himself circulated a similar sketch at the 1845jun meeting of the British Association for the Advancement of Science.

Himself's own caption for the similar sketch:

Fig. 25 Herschell ??? sketched April 1845, carefully confirmed with original on different nights but no micrometer ??? Handed around the section at the Cambridge meeting

Himself did, in fact, believe that the spiral nebulae were other galaxies??? (No-437).

Other sketches by Himself can be seen at Sandburg Center for Sky Awareness.

Credit/Permission: William Parsons, 3rd Earl of Rosse (1800-1867), 1845 / Public domain.

Image linked to Wikipedia.

Permission: Public domain at least in USA.

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Actually, there is a better modern analog to the VORTEX WORLDS.

The atomist theory of a vortex-world cosmology bears a passing resemblance to eternal inflation, a modern cosmological theory---albeit one with a lot more math. The universe domains being the modern analogs of the VORTEX WORLDS.

We discuss eternal inflation below in the section Inflation and Inflation Cosmology.

The cosmological theory that became dominant in Greco-Roman antiquity and then in the Islamic Golden Age (c. 9th--13th centuries) ...

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Caption: At the Alhambra in Granada, Spain: "A room of the palace and a view of the Court of the Lions."

Credit: Adolf Seel (1829--1907), 1892 / Public domain.

Image linked to Wikipedia.

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... and Medieval Europe ...

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Caption: Joan of Arc (1412--1419) (AKA Jeanne d'Arc, Jehanne, la Pucelle, the Maid of Orleans, Saint Joan).

Credit: Unknown French artist, circa latter half of the 15th century / Public domain.

Image linked to Wikipedia.

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... was that of Aristotle (384--322 BCE)---who was a post-Socratic philosopher.

Aristotle (384--322 BCE), the Supreme Authority.

In Aristotelian cosmology, the Earth was at the center of an eternal, bounded, finite, spherical universe.

The boundary was a real physical celestial sphere of the stars on which the stars were pasted: the planets were closer and held on compounded other celestial spheres which were moved by gods or in monotheistic contexts by angels.

A cartoon of Aristotelian cosmology.

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Caption: Dante Alighieri (1265--1321) and Beatrice in an illustration of the Paradiso of the Divine Comedy.

One cannot be certain how literally Dante took his description of the Heavens. He did refer at least to some aspects of the Divine Comedy as "the fable".

Credit/Permission: Gustave Dore (1832-1883), 1867 (uploaded to Wikipedia by User:Sailko, 2007) / Public domain.

Image linked to Wikipedia.

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Beyond the celestial sphere of the stars was nothing: not even empty space---even in Greco-Roman antiquity a lot of people found this "not even empty space" part hard to accept.






























What if you stood at the boundary of the celestial sphere of the stars and thrust a spear outward? What would happen? Aristotle gives no answer.

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Caption: A 4th century BCE hoplite.

Credit/Permission: Johnny Shumate, 2007 / Public domain.

Image linked to Wikipedia.

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Aristotelian cosmology actually bears a passing resemblance to the Einstein universe which we discuss below in the section Einstein, General Relativity, and the Einstein Universe.
One begins to wonder if cosmology is an endless recycling of old ideas---albeit with a lot more math.

The small Aristotelian universe was put in doubt to the astronomically-minded by Nicolaus Copernicus's (1473--1543) Copernican heliocentric solar system of 1543. First of all, by putting the Sun in the center of the Solar System, of course.
Question: Was Copernicus the first proposer of the heliocentric solar system?
1. Yes.
2. No. Some ancient Greek was first.
3. Maybe.








Answer 2 is right.

You are beginning to get the idea. Some ancient Greek has thought of everything first.

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Aristarchus of Samos (ca. 310 -- ca. 230 BCE): the first proposer of heliocentrism.

But Aristarchus only presented the bare idea of heliocentrism as far as we know although he probably knew some of the reasons why it was a good idea.

Copernicus is justly credited as the innovator since he presented a detailed argument that was somewhat convincing and was NOT ignorable.

This is often the way in the history of science.

The giver a convincing proof or argument gets more fame than the speculator---and this seems just.

Aristarchus is a precursor of a discovery--- a person who discovers something, but fails to make the world appreciate it's value---a prophet without honor in his time.

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Heliocentrism also upset the Aristotelian universe by requiring the fixed stars to be extremely remote: this is the only reasonable way that the Earth could move and the fixed stars not show stellar parallax in pre-modern observations.

But if the stars were very remote why should they be pasted on a big sphere?

Why not an infinity of stars spread throughout an infinite universe? or at least a quasi-infinity of stars spread throughout a quasi-infinite universe? Quasi meaning "seemingly" in this context.

In the context of Copernican heliocentrism, the idea of an infinity of stars spread throughout an infinite universe was first put forward by Thomas Digges's (1546--1595) in 1576 (No-296).

Others, like Democritus and Nicholas of Cusa (1401--1464), had considered infinite universes in the past, but not in the context of Copernican heliocentrism, of course.

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Caption: Thomas Digges's (1546--1595) illustration (presented in his treatise A Perfit Description of the Caelestiall Orbes according to the most aunciente doctrine of the Pythagoreans, latelye revived by Copernicus and by Geometricall Demonstrations approved, 1576) of a heliocentric solar system surrounding by an infinite space with stars spread throughout.

Infinite universes had been considered before, of course, but Digges to consider an infinite universe in the context of a heliocentric solar system.

Since the caption is in Elizabethan English, we can even read it sort of.

Isaac Newton (1643--1727) thought of the spread out stars as being the fixed stars which defined the fundamental inertial frame.

The colorization is modern.

Credit/Permission: Thomas Digges (1546--1595), 1576, Colorized by Jean Gagnon (AKA User:Jeangagnon), 2007 / Public domain.

Image linked to Wikipedia.

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As heliocentrism gained credence and the telescope revealed a quasi-infinity of new stars and that the Milky Way was a band of stars, the notion of an infinite or very large universe filled with stars became plausible.

The Sun could not be considered the center of this kind of universe. Sooner of later, it became clear the Sun was just another star---but it is our star.

Isaac Newton (1643--1727) certainly thought in terms of infinite or very large universe filled with stars (No-375). Or at least a quasi-infinite or very large universe filled with stars.

Newton of the Principia (1687).

In unpublished work, Newton tried to construct a physically consistent STATIC MODEL of such a universe---using Newtonian physics, of course (No-376).

"Physically consistent" means no violations of physical law. The initial conditions of a physically consistent model NOT necessarily real, and so the the model is NOT necessarily real.

His own theory of gravity suggested that matter would all collapse into a single clump at about??? the center of mass in any FINITE STATIC MODEL: the universe of stars couldn't exist as a static structure.

Could extending the universe to infinity with infinite stars result in a balance of forces that allow the universe to stand up? Maybe, but, in fact, Newtonian physics does not have a clear solution to this problem.

An essential problem is how does one deal with infinite quantities: e.g., infinite force and infinite mass.

But even making assumptions about how infinite quantities behave, it seems that in an infinite universe full of stars a balance would be an unstable mechanical equilibrium---any perturbation would start it evolving into clumps.

Newton didn't like to publish half-baked ideas, and this probably why he never published his cosmological ideas. He liked all-baked publications.

Attempts in the 19th century to create a Newtonian theory of the whole universe foundered: they were all based on the idea that the universe as a whole had to be STATIC on average even though it was known that stars actually do move around with their own peculiar velocities (Bo-75).

In fact, Newtonian physics does NOT seem to allow one to construct an infinite universe model, static or not, without new assumptions about physical laws (Bo-75,78).

But one could have an infinite space universe with a finite Milky Way rotating about its center.

Recall Thomas Wright (1711--1786) proposed that the Milky Way was supported against gravitational collapse by orbital motion about the center (the ``divine center'') of the Milky Way (No-405).

This cosmology didn't catch on for reasons that are not clear. It seems perfectly sensible.

People, starting with Newton, seem fixed with the idea that the universe should be STATIC overall.

Of course, Wright believed that there were other galaxies.

What if they existed? What would keep them from all collapsing into a clumps under self-gravity?

The modern attempts to frame a physically consistent theory of the universe started with Einstein and his general relativistic model of 1917: this is the Einstein universe (No-520; Bo-97) which we will discuss below in the section Einstein, General Relativity, and the Einstein Universe.
Early cosmology videos:
1. Ptolemaic vs. Copernican Model Requires instructor narration. Short enough for the classroom.
2. History of the Universe in a nutshell: Aristotle, Ptolemy, Copernicus, Kepler Too dull for class, but short.
3. 4 The Universe Aristotle and Ptolemy The History Channel's take---with a few words from Michio Kaku (1947--). Too long for classroom.
4. Carl Sagan - The Pioneers of Science 3/3 Carl Sagan (1934--1996)---he's everywhere---gives his take on Aristarchus of Samos (ca. 310 -- ca. 230 BCE)---``planets are not going arooouunnnd the Earth''. Too long for classroom.

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The Expansion of the Universe

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After the Copernican revolution of the 16th and 17th centuries, the idea of space as quasi-infinite with a quasi-infinity of stars gained ground and Newton believed it as we mentioned above.

The idea of space as quasi-infinite with a quasi-infinity of stars was the basic idea of vague cosmology that then existed from circa the 17th century on to the early 20th century.

The idea evolved through the history of the discovery of galaxies which was discussed in IAL 26: Discovery of Galaxies. This history is the essentially the history of observational cosmology from the 18th century until the 1920s.

Another basic idea of cosmology that persisted up to circa the 1920s was that the universe was essentially STATIC???: the stars and other galaxies (assuming they existed) were not moving on average even though stellar peculiar velocities were known. Without having a poll from the past it is hard to know how many astronomers thought this, but certainly it was held Einstein who evidently thought it was accepted theory.

This belief in a STATIC universe is actually odd since the universe was obviously NOT thermodynamically static: i.e., it is NOT in thermodynamic equilibrium:

Space (i.e., the main components of it, cosmic microwave background radiation (CMB) first of all) is cold (as evidenced by our own planet Earth) and stars are hot.

Heat energy is steadily being lost to stars as energy flows out of them in the form of electromagnetic radiation and not being returned.

Why should a system so obviously evolving thermodynamically be automatically assumed to be dynamically static on average? If evolving in one way, it could well be evolving in other ways?

Actually there was evidence in the early 1920s for large-scale motions.

Vesto Slipher (1875--1969) at Lowell Observatory in Flagstaff, Arizona, starting in 1912 had been measuring the spectral shifts of galaxies (No-522--523). He didn't know they were galaxies for sure until Hubble's convincing proof the extragalactic nature of the spiral nebulae in 1923.

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Caption: The Slipher Rotunda Museum at the Lowell Observatory in Flagstaff, Arizona.

This may be the dome where Vesto Slipher (1875--1969) discovered the systematic cosmological redshift of the galaxies---but no one's telling.

Despite spending a year Flag (2010 Aug--2011 May) and visiting the Lowell Observatory several times, yours truly never noticed the Slipher Rotunda Museum---your truly was probably just being obtuse.

Also in my days in Flag, I learnt that old Vesto was also a real estate developer---West Saturn Way, Meteor Drive---he made a killing.

Credit/Permission: Leslie Connell, 2006 / Public domain.

Image linked to Wikipedia.

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By 1925, Slipher had spectral shifts for 45 galaxies. There were a few blueshifts, but most were redshift.

Interpreted as Doppler shifts---which, in fact, is NOT exactly right, though that is what was assumed originally by Slipher and, perhaps for awhile, by Edwin Hubble (1889--1953)---these results showed that most galaxies (the redshifted ones) were moving away from ours and using the Doppler shift formula their recession velocities were known. The blueshifted galaxies are moving toward us.

The spectral shifts are actually a mixture of Doppler shifts due to relatively small peculiar velocities (relative to inertial frames that participate in the mean expansion of the universe) and cosmological redshifts due to the expansion of the universe.

For the blueshifted galaxies, the Doppler shift dominates: these are nearby galaxies that do not participate or not very much in a cosmological expansion relative to us.

As distance from us increases, the cosmological redshift part grows greater and soon becomes completely dominant.

The Doppler effect and the cosmological redshift are closely related in a sense and they coincidentally have the same 1st order formulae for relatively small shifts, and thus unclarity about which effect applied did NOT wrong-track people much in the 1920s.

The Doppler shift formula worked well enough to give accurate recession velocities for the relatively nearby galaxies for which they could measure spectral shifts for in those days.

But the effects are distinct though many textbooks confuse them.

The Doppler effect is caused by relative motions.

The cosmological redshift is caused by the growth of space under light as light travels through it. This growth stretches the wavelength of light: i.e., redshifts it.

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Cosmological redshift illustrated.

Cosmological redshift quantity z is defined by the formula

  z=(λ_observed-λ_rest)/λ_rest  ,

  where λ_observed is observed wavelength
  and λ_rest is the wavelength in the rest frame of emission.
  

The redshift velocity is given by the formula

  v=zc  , where
         c is vacuum light speed.

        This formula has the same form as the 1st order
        Doppler effect formula.

For the local universe (i.e., z ≤ 0.5), the redshift velocity and recession velocity are approximately equal, becoming exactly equal in the limit that z goes to 0.
This is why we say that the 1st order Doppler effect and the 1st order cosmological redshift formula are the same to 1st order.

In fact, for the local universe, redshift velocity and recession velocity are often NOT clearly distinguished either for simplicity---as yours truly does---or for confusion.

Except for the local universe, recession velocity is NOT a direct observable.

For the local universe, recession velocity is the directly measured redshift velocity.

Got that.

---

Question: Were the spiral nebulae known to be other galaxies by 1925?
1. Yes.
2. No.
3. Maybe.











Answer 1 is right.

In 1923, Hubble had shown that the Andromeda spiral nebula (M31) was another galaxy and by implication all other spiral nebulae were too (No-510).

Figuring out that ellipticals were other galaxies must have happened immediately. Ellipticals occur in galaxy clusters with spirals. Assuming a physical association for galaxy clusters---which would be inescapable, I'd say---the conclusion is that ellipticals must be extragalactic too. This must have been clear from 1923 on.

One has to add that people do NOT necessarily assimilate new information immediately. This is true today and more so in the past.

So Hubble's discovery may not have been assimilated by some astronomers for some years. Even if they had heard of it, they may have resisted believing it for any number of reasons---like being old stick-in-the-muds.

But what was the FLOW PATTERN of the receding galaxies?

To know this you had to know, in addition to recession velocities, distances to the galaxies: i.e., where the galaxies were in space.

By 1929, Hubble had the distances by various means to 18 galaxies beyond the Milky Way (No-510).

Recall Hubble with the 100 inch (2.54 m) Hooker telescope at the Mount Wilson Observatory in southern California (before most of the smog and light pollution) had the best observing technology of his time (No-439).

This was essential to his discoveries.

He could only use Cepheids as distance indicators for the nearest galaxies: maybe the only large galaxies they could be used for are the Andromeda galaxy (M31, NGC 224) and Triangulum galaxy (M33 or NGC 598). That is about as far as he could observe them???. (See also IAL 26: Cepheids).)

Hubble had to use cruder methods for more remoter galaxies. Those methods had large random and systematic errors and random errors.

So his distances were not too good---but they were good enough for his most famous discovery.

---



Caption: "The 100 inch (2.54 m) Hooker telescope at Mount Wilson Observatory near Los Angeles, California. This is the telescope that Edwin Hubble (1889--1953) used to measure galaxy distances and discover the general expansion of the universe. At the time of this photograph (1989), the Hooker telesscope had been mothballed, although in 1992 it was refitted with adaptive optics and is once again in use."

Credit/Permission: © Andrew Dunn (AKA User:Solipsist), 1989 / Creative Commons CC BY-SA 2.0.

Image linked to Wikipedia.

---

Using Slipher's spectral shifts and maybe other spectral shifts, Hubble was able to find a remarkably simple relationship between distance and recession velocity (No-523).
He may have still been interpreting the shifts as Doppler shifts then, but maybe not. Hubble was to some degree aware of the developments in theoretical cosmology which were going in the during the time of his important discoveries: see section Friedmann-Lemaitre Models below.

However, as described above, the 1st order Doppler shift formula, is coincidentally correct for the 1st order cosmological redshift.

The observational relationship found by Hubble, first presented in 1929, is now called Hubble's law:

      v=Hr  , where 

      v is recession velocity nowadays measured in km/s,
      r is distance nowadays measured in megaparsecs,
      and H is a constant, now called the 
         Hubble constant---but
         it's only constant in space in theory---in cosmic time, 
         it varies in theory.

      Hubble's original value for H was

        540 (km/s)/Mpc (Bo-39).

      Hubble had considerable systematic distance errors, and so his
        value was rather badly wrong.

      Even today, the 
      value of the Hubble constant 
      has not been absolutely
      agreed on with values ranging between about 64 and 80 (km/s)/Mpc 
      (see Wikipedia:  Hubble's law:  Determining the Hubble constant). 

      However, the extreme values (64 and 80) seem very doubtful nowadays.
      
      For this lecture, we will use
      70.4(1.4) (km/s)/Mpc, where 1.4 is the error in the last digits
      (see Wikipedia:  Concordance model:  Parameters).
      The concordance model
      (which we discuss below in the section 
      Big Bang
      to the present.
      The theoretical significance of the
      concordance model
      may change, but its description of motion is likely to 
      be close to the truth. 

      Or we will write H=70*h_70 (km/s)/Mpc, where h_70=H/(70 (km/s)/Mpc) if a fiducial reduced 
      Hubble constant.
      This is a standard way of writing the 
      Hubble constant
      leaving the actual value general, but indicating a fiducial value, in this case 70 (km/s)/Mpc. 

Hubble's law shows that there is a general expansion of the universe and that the rate of expansion (actually the rate of expansion per megaparsec) is the Hubble constant.

So Hubble had observationally discovered the expansion of the universe---but with a little qualification to acknowledge Knut Lundmark (1889--1958).

---



Caption: "Portrait of Swedish professor Knut Lundmark (1889--1958) as student 1908, with signature."

This looks like a graduation picture of some kind.

Lundmark anticipated Edwin Hubble (1889--1953) with evidence for the expansion of the universe and Hubble's law in 1924 with galaxy distance measurements that were, in fact, much more accurate than Hubble's as we now know (Steer, 2012).

His value for the Hubble constant is very to the modern one of H=70.4(1.4) (km/s)/Mpc. Hubble's own original value of H=500 (km/s)/Mpc is very inaccurate (Tamann 2005).

The superior accuracy of Lundmark's results seem to be partially based on luck and partially on a then unverifiable method of using galaxy angular diameter distances.

Hubble, of course, was the person who provided the convincing proof the expansion of the universe and Hubble's law. Which is why he gets the credit for these empirical discoveries.

But it seem that Lundmark deserves half the credit.

If the contingencies of history had worked out otherwise (i.e., people had accepted Lundmark's results right away just by chance), then we might today have Lundmark's law and Lundmark's constant.

Credit/Permission: Unknown photographer at H. Tegstroem & Co., 1908 / Public domain.

Image linked to Wikipedia.

---

Hubble extracted Hubble's law from what we now call a Hubble diagram.

See the example Hubble diagram just below.

---



Caption: A Hubble diagram of galaxies for the local universe.

A Hubble diagram is a plot of recession velocity plus peculiar velocity versus cosmological physical distance for extragalactic astro-bodies.

For the local universe, the axis quantities are the same (to within in some error that goes to zero as cosmological redshift z not counting any peculiar velocity contribution) goes to zero) as, respectively, redshift velocity and luminosity distance. Which is very useful because redshift velocity and luminosity distance are direct observables and recession velocities and cosmological physical distance are NOT in general.

A Hubble diagram insofar as the peculiar velocities can be neglected illustrates Hubble's law (which follows from the expansion of the universe):

 v=Hr  ,  where
          v is recession velocity,
          r is cosmological physical distance,
          and 
          H=70.4(1.4) (km/s)/Mpc is the
          Hubble constant.
            (see Wikipedia:  Concordance model:  Parameters).
          

Actually, this Hubble diagram is for galaxies too close to Milky Way to show clearly Hubble's law behavior. The peculiar velocities sometimes dominate over recession velocities which are due to the growth of space which is the expansion of the universe.

This is shown clearly by the data points for the Virgo Cluster. They do NOT follow the straight line predicted by Hubble's law . The galaxies of the Virgo Cluster orbit approximately the center of mass of the Virgo Cluster, and the components of those orbital velocities (plus any other contributions to the peculiar velocities) along the line of sight from Earth get added to cosmological redshift velocities to give the observed redshift velocities.

In fact, the data are from such close galaxies that it may be somewhat accidental that the data points follow the straight line as well as they do.

For much more remote galaxies, the peculiar velocities become negligibly small compared to the recession velocities and one gets clear Hubble's law behavior.

Of course, if one gets too remote (i.e., to z approximately ≥ 0.5 which is beyond the local universe according to the concordance model), the directly observed redshift velocities and luminosity distance cease to follow Hubble's law. Recall the concordance model is a very adequate description of the observable universe insofar as it can be verified.

However, in expanding universe cosmology, Hubble's law holds for all cosmological redshifts for recession velocity and cosmological physical distance.

Actually, yours truly thinks that it would have been better to have plotted distance versus cosmological redshift z (plus any Doppler effect redshift) because redshift is the more easily measured direct observable than distance. Then "Hubble's law" would have been

               r=zr_H  ,

                    where r_H is a distance parameter equal to c/H which is called the
                    Hubble length,
                    in fact.
          

This "Hubble's law" would have made writing various formulae easier. On the other hand, this "Hubble's law" holds only for the local universe, and so is less general.

Credit/Permission: © User:Brews ohare, 2009 / Creative Commons CC BY-SA 3.0.

Image linked to Wikipedia.

---

In the Hubble diagram just above, the line is the representation of Hubble's law and the slope of the line is the Hubble constant.

Hubble's law shows that there is a general growth of distances between extragalactic objects when the redshift of remote objects is correctly interpreted as the cosmological redshift.

As mentioned above, this general growth is called the expansion of the universe.

Question: In the Hubble diagram there is a scatter about the straight line.
1. This is caused by observational error.

2. The gravitationally bound systems are not internally expanding and their components have rather random peculiar velocities which add Doppler shift to the cosmological redshift (due to the expansion of the universe) to create net spectral shifts. The redshift velocities thus have deviations from the straight line.

3. The gravitationally bound systems as wholes have their own rather random peculiar velocities which add Doppler shift to the cosmological redshift (due to the expansion of the universe) to create net spectral shifts. The peculiar velocities thus have deviations from the straight line.

4. The recession velocity is not exactly linear as a function of distance. There are deviations from linearity.













The first 3 answers are all partially right. Together they constitute what we believe to be the right answer.

So far observationally everything indicates the recession velocity (not recession velocity plus peculiar velocity) is exactly linear with distance for sufficiently small cosmological redshift z.

How small is sufficiently small depends on the cosmological model adopted.

But the concordance model (which is the standard model at present) sufficiently small is z approximately ≤ 0.5 which is our definition of the local universe. See Cosmological Distance Measures Graph.

We discuss cosmological models below: see section Einstein, General Relativity, and the Einstein Universe and subsequent sections.

In fact, these models predict Hubble's law is exactly right for our universe or universe domain for recession velocities and distances measured at exactly one instant in cosmic time (CL-14,47).

Distances measured at one instant in cosmic time are called cosmological physical distances or, just physical distances for short.

But we CANNOT verify Hubble's law for large physical distances by direct observations.

This is because the at-one-instant-in-cosmic-time recession velocities and physical distances are not direct observables beyond the local universe (which is defined by z approximately ≤ 0.5). They are dependent on the cosmological model adopted, and so have that model's uncertainty.

We can't observe galaxiescosmic time, but only as they were in the past.

Cosmic time is the time in which the expanding universe stays homogeneous and isotropic.

Also all clocks participating in the mean expansion of the universe stay synchronized with cosmic time.

How the universe evolves with cosmic time is, of course, dependent on the cosmological model adoped.

Well the universe evolves in only one way with cosmic time, but how understanding of how it evolves is model-dependent---but you knew this already.

Cosmic time doesn't flow very differentally from local universe times (including Earth-based times) since the deviations of local universe motions from the mean expansion of the universe are rather small.

So we think we can measure cosmic time accurately locally, but we don't know what the cosmic time is for cosmologically distant objects at the time light was emitted from them independent of the cosmological model adopted.

Question: Hubble's law implies that:
1. the Milky Way is the center of cosmic expansion.
2. the expansion is a general scaling up of distances between non-gravitationally bound systems. All observers participating in the mean expansion of the universe located in bound systems see the same expansion behavior on average. Such ideal observers are approximated by those in the gravitationally bound systems.












Well either answer could be right logically speaking.

But answer 2 is so overwhelmingly more acceptable that we must accept it as right.

There is ASSUMPTION in cosmology called the Copernican principle: it states that we occupy NO special place in the universe. This principle is a guiding simplifying principle in cosmology.

We have no observational evidence or broadly accepted theoretical reason for thinking it is false. In fact, as far as we can tell it seems true.

The following diagram shows how to understand general expansion.

The universal expansion.

Is there a center of expansion?

In Friedmann-Lemaitre models (see section Friedmann-Lemaitre models), there is NOT. The expansion is everywhere and started from a state of infinite density or very high density which was everywhere. Everywhere has grown. The universe has just been growing and is NOT expanding into anything.

On other hand, maybe there is a center somewhere in some sense, and the Friedmann-Lemaitre models or whatever models are correct, describe only a portion of the universe and there is an expansion into something beyond in some sense. Such a universe would NOT homogeneous and isotropic as our universe seems to be. But maybe our universe is only approximately homogeneous and isotropic over the scales we can observe.

We don't really know if there is in any sense a center of universal expansion or not.

Universal expansion leads to quandaries Newtonian physics:

1. Newton postulated an absolute, infinite space. A finite system of galaxies can expand in this infinite space and would decelerate under self-gravity.

   Such a finite system of galaxies could not be homogeneous nor isotropic.

   It must at least have an outer boundary to the system of galaxies beyond which empty space stretches forever.

   We see no evidence for inhomogeniety or anisotropy when we observe the universe on the largest scale we can.

   Also why should there be a finite system of galaxies in an infinite universe?

   Just so?

   But scientists don't like just-sos.

2. If there is an infinite system of galaxies spread through an infinite space, there is no solution in pure Newtonian physics for the behavior of the system as we mentioned in the section The Early History of Cosmology.

   Extra ad hoc hypotheses could be invented to supplement pure Newtonian physics to give solutions for the behavior.

   But those ad hoc hypotheses could be chosen to give any behavior we like. They don't predict the behavior.

   Therefore, those hypotheses are not strongly supported by the observations.

   In science, an ad hoc hypothesis means one just invented to solve a special-case problem or give fit special-case behavior. Such hypotheses may turn out to be right, but since they were invented for special cases, they are likely to turn out to be wrong. The experience of the whole history of science shows this.

   An non-ad-hoc hypothesis is one that has a general applicability---of course, non-ad-hoc hypotheses are often wrong too, but they are easier to prove wrong and they are more fruitful in suggesting how to advance the research.

In fact, SEMI-NEWTONIAN COSMOLOGICAL MODELS (with modified Newtonian physics) have been invented which are have some consistency with the observable universe (Bo-75), but we know Newtonian physics is less correct than relativistic physics.

So those SEMI-NEWTONIAN COSMOLOGICAL MODELS cannot be correct if they are not consistent with relativistic physics---which they arn't---unless there are strange factors we are unaware of.

The SEMI-NEWTONIAN COSMOLOGICAL MODELS are, however, interesting historically and very useful pedagogically---but we won't pedagoge on them.

---

To summarize this section, we have the observed expansion of the universe. Since the universe seems homogeneous and isotropic, there is no apparent center of expansion and NO reason to believe the universe is expanding from some region or expanding into any region.

As far as we can tell observationally, expansion of the universe is a general scaling up of distances between gravitationally unbound systems.

We also know that general relativity (GR) is our best theory of gravity and spacetime.

So how do we explain the universe and the expansion of the universe?

We'll see in the sections below.

---

Cosmological Distance Measures Explained

---

At this point, we are going to temporarily break off our historical discussion to cover cosmological distance measures.

We have will have anticipate some of the history and material from later sections of this lecture, in particular, the concordance model which has been developed since circa 1998.

It's too much of Procrustean bed to be strictly historical.

---



Caption: "The exquisite, gilded bier on which Egyptian pharaoh Tutankhamun's nest of coffins rested, within his sarcophagus. It is now on display at the Cairo Museum."

A bit rich for Procrustes, but it looks like a Procrustean bed to me.

Credit/Permission: © Hans Ollermann, 2004 / Creative Commons CC BY-SA 2.0.

Image linked to Wikipedia.

---

We will return to history afterward.

In fact, this section became so monumental/overwrought that your truly decided to hive it off to its own file IAL 31a: Cosmological Distance Measures Explained.

IAL 31a is part of this lecture's required reading.

???? Revise below into 31a ????

Before going on to specific theories of the universe, it is useful to consider two characteristic quantities: the Hubble time and the Hubble length.

Hubble's law can be rewritten

     r=v(1/H) ,

from which one can see that 1/H must have the units of time.

If the recession velocities are CONSTANT in time, 1/H is the time since all the matter in the expanding universe was clumped together with infinite density.

We call 1/H the Hubble time.

An epoch of infinite density is a singularity in which our laws of physics (including modern physis) fail.

In fact, the singularity at the beginning of the universe is one meaning of the term Big Bang, but that's not the modern primary meaning.

Whether there was an actual singularity at the beginning of the universe (or our universe domain) is moot, but most cosmologists (I think) think there was NOT.

They do think the Big Bang happened in the other meaning of the term: a time of very high density and temperature which was at the beginning of our universe (or universe domain).

We discuss the Big Bang in its primary meaning in following sections.

The term singularity is still used to describe time zero of the Friedmann-Lemaitre models which are the class of model that best describe our universe (or universe domain)---but only at some very small time (much less than 3 minutes) after the singularity.

The actual evolution of the universe is thought to track into the Friedmann-Lemaitre models. We still count cosmic time from the the time zero of the Friedmann-Lemaitre models. It is sort of a fiducial time zero.

The concordance model is the current favored Friedmann-Lemaitre model and is likely to remain so with only small adjustments to its parameters.

We take that time zero as being the fiducial time zero of cosmic time for our universe (or our universe domain).

We discuss the Friedmann-Lemaitre models in the section Friedmann-Lemaitre Models and following sections.

Now the recession velocities are very probably NOT constant.

But for the universe (or our universe domain), the Hubble time 1/H should be a characteristic age of the universe in Big Bang cosmological models (which we discuss below in the section Friedmann-Lemaitre Models and subsequent sections): i.e., 1/H should be order of the cosmic time since the Big Bang (in the primary meaning of the term).

We will in fact from here on always assume Big Bang cosmological models (which we discuss below in the section Friedmann-Lemaitre Models and subsequent sections) since there is very good evidence that they are close to true for the observable universe and they are the only models for the observable universe widely considered at present.

Using H=70*h_70 (km/s)/Mpc, where h_70=H/(70 (km/s)/Mpc) if a fiducial reduced Hubble constant (which is actually known to be 1 to with a few percent from the concordance model),

      1/H =              1                   3.08567758*10**19 km
               _________________________ *   _____________________
	         70 (km/s)/Mpc * h_70              1 Mpc

           = 4.41*10**17 s  / h_70

           = 14.0  Gyr / h_70.

Question: If we could freeze the expansion right now, from how far away could light reach us in a Hubble time? Remember distance equals velocity times time for constant velocity.
1. 10 Mpc.
2. 4283 Mpc / h_70.
3. c/H.











Answer 3 and answer 2 is right too.

c/H=c*(1/H) is just the vacuum light speed times the Hubble time.

We call c/H the Hubble length:

     r_H = c/H =    2.998*10**5 km/s
                 ______________________
	           70 (km/s)/Mpc * h_70 

         = 4283 Mpc / h_70 .
	     

Given that the Hubble time is a characteristic age for the universe, the Hubble length is a characteristic size scale for the observable universe.

Signals from very much farther away than a Hubble length could NOT have reached us since the Big Bang.

The observable universe is the largest sphere centered on us that is CAUSALLY CONNECTED to us.

Matter NOW (i.e., at our instant in cosmic time) located at the radius of the observable universe could have emitted at light signal at the time of the Big Bang that would reach us NOW. The radius of the observable universe is called the particle horizon which in a second meaning is the surface of the observable universe.

A light signal from matter within/beyond the particle horizon would/would not have reached us by NOW if it had started at the time of the Big Bang. In the "would" case it starts at the lookback time corresponding to its cosmological redshift z.

The matter at the particle horizon is unobservable as it NOW is. We can only see it as it was at the time of the Big Bang.

A light signal that started from matter NOW from the particle horizon may or may not reach us in the far future depending cosmological model adopted.

The radius from which a light signal starting NOW will reach us in the far future is called the cosmic event horizon (see also Wikipedia: Particle horizon).

Both particle horizon and cosmic event horizon are model-dependent quantities.

In the concordance model, particle horizon is about 14000 Mpc (see Wikipedia: Observable universe) and the cosmic event horizon is about 5000 Mpc (Wikipedia: Faster-than-light: Universal expansion).

Both these special radii are larger than Hubble length r_H=4283 Mpc / h_70. The cosmic event horizon radius is comparable to the radius of the local universe as we have defined it.

The Hubble length and the observable universe.

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Caption: A simulated view of the observable universe with particle horizon 14000 Mpc and observable universe diameter 28000 Mpc.

The Hubble length r_H=4283 Mpc / h_70 is a bit less than a third of the particle horizon.

Credit: © Andrew Colvin AKA User:Azcolvin429. Creative Commons CC BY-SA 3.0.

Image linked to Wikipedia.

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Actually, the observable universe as defined is NOT entirely entirely observable at present.

The universe becomes opaque to most light as one looks back in time to with about 400,000 years of the Big Bang.

We discuss this opaqueness below in the section Big Bang Cosmology and the Constituents of Observable Universe.

Some band of electromagnetic radiation or neutrinos or gravitational radiation will allow in principle observations to early epochs.

At present, these other radiations are not detectable.

Neutrinos may be the most hopeful case.

The universe is estimated to have become transparent to neutrinos at a cosmic time of about 2 s after the fiducial time zero of cosmic time (i.e., the time of the Big-Bang singularity). These neutrinos should have a temperature of about 2 K now and have a density of order 4*10**8 per m**3. But neutrinos are very hard to detect and the cosmic neutrino background has not yet been detected (FK-669).

Question: Actually, our definition of the Hubble length L_H=c/H raises a bit of a paradox.

By Hubble's law itself v=Hr (which as we argued above is exactly true for recession velocities and proper distances measured at one instant in cosmic time), a galaxy a Hubble length away should be moving RECESSION VELOCITY c.

Galaxies further away that a Hubble length should have RECESSION VELOCITIES greater than c.

But this result seems to violate special relativity.

1. Yes, it is a violation and something is wrong with our thinking.

2. The recession velocities are NOT ordinary velocities, but rates of growth of space between gravitationally bound systems. This growth rate can exceed the vacuum light speed according to general relativity.





Answer 2 is right in relativistic theory, but you probably didn't know that---except that the question is rather leading.

Do we see objects with recession velocities greater than c?

Yes, but exactly which objects have this property is dependent on the cosmological model one adopts.

In the currently favored concordance model (see section The Concordance Model below), objects at cosmological redshift z ≥ about 1.4 have current recession velocities greater than c.

Cosmological redshift z is, in fact, the usual way to specify the location of the remote objects since it is a direct observable:

             z=(lambda-lambda_0)/lambda_0 ,  

                                      where lambda is observed wavelength,
                                      and lambda_0 is the emission wavelength which
                                      is known from laboratory measurement of the
                                      spectrum lines of atoms.
    

We observe remote, and therefore long ago, galaxies, gamma ray bursts, quasars, etc. at much higher redshifts. Cosmological redshift z=1.46 is at a lookback time of about 9 Gyr in the concordance model (see Cosmological Distance Measures Graph).

In 2012, the records for some classes of interesting objects (see Wikipedia: List of the most distant astronomical objects) are:

1. z=10.3, galaxies.
2. z=9.4, gamma ray bursts,
3. z=7.085, quasars
4. z=2.357, supernovae.

These days, the record usually get broken pretty frequently.

A map showing the cosmological redshifts of the relatively nearby observable universe is shown below.

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Caption: "Panoramic view of the entire near-infrared sky reveals the distribution of galaxies beyond the Milky Way. The image is derived from the 2MASS Extended Source Catalog (XSC) (more than 1.5 million galaxies) and the Point Source Catalog (PSC) (nearly 0.5 billion Milky Way stars). The galaxies are color coded by cosmological redshift z obtained from UGC, CfA Redshift Survey, Tully NBGC, LCRS, 2dF Redshift Survey, 6dFGS, and SDSS (and from various observations compiled by the NASA/IPAC Extragalactic Database), or photo-metrically deduced from the K band (2.2 m). Blue are the nearest sources (z < 0.01), green are at moderate distances (0.01 < z < 0.04), and red are the most distant sources that 2MASS resolves (0.04 < z < 0.1). The map is projected with an equal area Aitoff projection (but Hammer projection seems to be meant) in the Galactic coordinate system (Milky Way at center)."

The image is in Hammer projection I suspect. This maps a spherical surface into an 2:1 ellipse. The shapes of regions are distorted, but their areas are accurate in some fastion.

The Milky Way obstructs the view of the large-scale structure of the universe in the image and in reality. The Milky Way can't be removed from the image without leaving some sort of artificial blank.

The filaments, voids, and foamy nature of the large-scale structure of the universe are made somewhat visible in image.

The cosmological redshifts or, for closest objects, distances in megaparsecs are given in parentheses for labeled galaxies, galaxy clusters, and galaxy superclusters.

For the local universe (i.e., z ≤ 0.5) cosmological physical distance approximately equals 4000*z. This follows from Hubble's law:

 v=Hr  ,  where
          v is recession velocity,
          r is cosmological physical distance,
          and
          H=70.4(1.4) (km/s)/Mpc is the
          Hubble constant.
            (see Wikipedia:  Concordance model:  Parameters).

 One inverts to get

 r=v/H=zc/H≅4000*z  ,  where
          we have used the approximate equality of
          recession velocity
          and redshift velocity
          (which is zc) for the
          local universe.
          The vacuum light speed c is
          exactly 2.99792458*10**5 km/s ≅ 3*10**5 km/s. 
          

The Virgo Supercluster includes the Virgo Cluster. The Virgo Supercluster is, otherwise, not labeled on the image on think.

Credit/Permission: NASA, IPAC/Caltech, Thomas Jarrett, 2004 / Public domain.

Image linked to Wikipedia.

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---

Einstein, General Relativity, and the Einstein Universe

---

In 1905, Albert Einstein (1879--1955) presented his theory of special relativity which among other things gave the vacuum light speed as the highest physical speed and showed that the flow of time was frame-dependent.

But special relativity does NOT explicitly deal with gravity.

Also Newtonian gravity as usually concieved before Einstein had its effects transmitted instantly. If you moved an object, its gravitational field (which is the cause of the gravitational force) moves instantly no matter how from the source object. This violated Einstein conclusion that the vacuum light speed was the highest physical speeds. So Einstein had to believe there was something incorrect about Newtonian gravity.

In order to remedy the problems with Newtonian gravity, Einstein went on a 10 year excursion into tensors and differential geometry and emerged in 1915 with general relativity (GR) which we have already introduced in IAL 25: Black Holes. (See also (St. Andrews Mathematics Archives: Einstein biography.)

The Einstein field equations are a main component of GR.

It was natural for Einstein to see if GR could be used to construct a model of the universe as whole.
``Natural'' in the sense that one often tries to apply new theories to systems of great interest to which the new theories should be applicable.

He came up with the Einstein universe, as we now call it, first presented in 1917 (No-520; Bo-97)

The Einstein universe is, in fact, probably the first universe model developed from an exact mathematical physics theory and completely consistent with that exact mathematical physics theory---except for the cosmological constant (see below).

Recall pure Newtonian physics is not able it seems to yield a consistent physical model of the universe as whole (Bo-75,78).
Well not a static one nor one in general expansion or contraction.

A finite system of galaxies held from collapse by rotation in an infinite, otherwise empty outer space seems possible to me.

Actually, Einstein earlier in 1917 presented an earlier GR universe model called the cylindrical model where space has the geometry of a 3-dimensional surface of a 4-dimensional cylinder (No-513). The cylindrical model never had much of a vogue though---it made the universe anisotropic??? for which there is no evidence.

In order to apply GR to the universe, Einstein made two major simplifying assumptions which are still usually used today at least for theories of our universe (or our universe domain):
1. The cosmological principle which is a glorified expression for the assumption that the universe looked at or averaged over sufficiently large scales is homogeneous (i.e., the same everywhere at one time) and isotropic (i.e, the same in all directions).
   We believe the cosmological principle is true for the observable universe, but you must look at and/or average over sizes of order 200 Mpc (CM-446; FK-596). Einstein did NOT know this in 1917, of course.

2. The mass-energy of the universe can be approximated a homogeneous, isotropic, pressureless perfect fluid (CL-33,40). We don't have to go into the exact specifications here.

Question: When starting out to model a complex system, one:
1. assumes a highly simplified picture in order to capture the essential behavior, and then afterwards adds complex features as needed to match observation.

2. just experimentally determines how the complex system behaves and one's understanding constitutes a working model which tells you pretty completely how to manipulate the system.

3. a bit of both 1 and 2 is often a good strategy: the weighting of the mixture depends on the case.





There is NO right answer, of course.

Answer 2 is essentially how traditional technologists solved their problems: e.g., building the pyramids, building cathedrals, sailing the Pacific Ocean in outrigger canoes.

However, in dealing with the extremely advanced systems of the modern age answer 3 has usually been pursued.

But when you can't experiment, as in cosmology, answer 1 is about what you are stuck with.

You realize your first attempts may be too simple or just plain wrong, but you have to start WITHOUT complexities that you don't know how to deal with anyway: i.e., crawl before walking.

Einstein, deferring to contemporary 1917 astronomical opinion, thought the universe should be STATIC. He took this as an ASSUMPTION.

Why a good physicist like Einstein---to say the least---should defer to a bunch of astronomers is beyond me especially since the obvious non-thermodynamic equilibrium state of the universe (which we discussed above in the section The Expansion of the Universe) pointed to an evolving universe.

Einstein also wanted to conform to Mach's principle and that also led to a static universe??? (Bo-97--98; Fre-543). But we won't worry about this esoteric point.

Einstein could NOT find a STATIC MODEL with GR as he had originally proposed it (No-520).

But by introducing a new term into the Einstein field equations---the cosmological constant---he could get a STATIC MODEL by fine-tuning the constant to provide a repulsion that exactly canceled the attraction of gravity.

The repulsion could be considered at kind of anti-gravity, but its not what one ordinarily means by that term and no one calls it that or a kind of negative pressure which is how we think of it nowadays though Einstein may not have.

The cosmological constant as a mathematical symbol is the capital Greek Lambda Λ.

Often one just says Lambda instead of the cosmological constant.

Below we sometime say the cosmological constant Lambda for clarity.

As well as Λ for Lambda, we will also need the capital Greek letter Ω for the density parameter symbol Ω: see below.

Often we just say Omega for the density parameter.

For reference, below is the Greek alphabet.

---



The Greek alphabet: alpha, beta, gamma, ... ---you get it right.

---

The cosmological constant was an ad hoc hypothesis to obtain a STATIC MODEL, but at least it was just about the simplest modification of the Eistein field equations that one could imagine and it was sufficiently small that it had no significant effect on any other gravitational phenomena.
Physicists use the expression fudge factor for a quantity one just inserts into a calculation to get the answer one expects---fudge factor because one cooks it up.

Students too are quite adept at creating fudge factors on tests.

The cosmological constant is arguably a fudge factor.

On the other hand, it satisfies Occam's razor in that is the simplest and most natural way of getting a STATIC MODEL of the universe from the Eistein field equations.

It is not cause of hodge-podge of hypotheses that have little chance of being right.

So it could be argued that cosmological constant STATIC MODEL had some chance of being right if Einstein's assumption of a static universe had been right.

The STATIC MODEL is now called the Einstein universe. It is the 3-dimensional surface of a 4-dimensional hypersphere: i.e., it is finite, but unbounded, hyperspherical space (No-520; Bo-98).

The 4th spatial dimension is given no physical interpretation: there is nothing imagined off the 3-dimensional surface.

Now we have difficulty picturing curved 3-dimensional spaces, but the 2-dimensional analogs of curved spaces can pictured.

I wonder how well we picture 3-dimensional flat space. Maybe we only picture it in the sense that experience tells us how things look in other directions from the one we are viewing an object from.

---

2-dimensional space analogs of possible geometries of space in simple GR models of the universe.

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Omega is a density parameter that determines the curvature of the space in GR. We will discuss it below in the section Friedmann-Lemaitre Models and subsequent sections.

The Einstein universe is analogous to the surface of an ordinary sphere in the diagram above.

In such a space traveling in a straight line (a line that seems to be straight at every locality) should bring you back to where you started and if you looked long enough you should see the back of your head.

The Einstein universe is actually in unstable equilibrium (Bo-118; No-527). Any perturbation will start it on runaway expansion or contraction.

Below is a cartoon that illustrates stable and unstable equilibriums.

Stability of a mechanical system.

Exactly how the many local perturbations that exist in the real universe could have affected a real Einstein universe is hard to say. But for awhile a universe evolving away from a static Einstein universe was a well considered model of the expanding universe (No-527).

After 1929 and the observational discovery of expansion of the universe (No-523) and discussions with Hubble in 1930 (No-526), Einstein abandoned his model and subsequently said (probably pretty often, but certainly to George Gamow (1904-1968)) that inventing the cosmological constant was the biggest blunder of his life.
He certainly meant his scientific life, not his private life. Einstein wasn't a good family man, in fact: late in life he commented that he had failed at marriage twice and that was his greatest shame.

Question: What Einstein meant about his biggest blunder was that:
1. the cosmological constant was a simple math error.
2. he had NOT trusted his own original formulation of general relativity, and thereby missed his chance to predict the expansion of the universe and have a better model of the universe than the Einstein universe.












Answer 2 is right.

The cosmological constant was a mistake in its original use, but it didn't go away.

It continued to be useful in for other cosmological fix-ups---``the refuge of scoundrel cosmologists''---and in fact it has come back in a new function with a vengeance as we'll see below the section The Accelerating Universe and the Friedmann-Lemaitre-Lambda Models.

But though Einstein blundered, others did not: expansion of the universe was predicted from GR models before it was observationally discovered.

Einstein videos:
1. Albert Einstein (02) Probably from circa 1930. This may have been when his discussion with Edwin Hubble (1889--1953) and others at Caltech led to his abandonment of the cosmological constant. The newsreel says this is a return visit, and so maybe this was after the abandonment of the cosmological constant. Not too interesting, but short enough for the classroom.
2. E=mc**2: Einstein explains his famous formula Too long for the classroom.
3. The Accelerating Universe: Einstein's Blunder Undone Bob Kirshner (1949--) gives a Behte lecture. Too long and off the topic mostly.

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Friedmann-Lemaitre Models

---

Alexander Alexandrovich Friedmann (1888--1925) in Russia in the early 1920s and Georges Lemaitre (1894--1966) in Belgium just a bit later and independently developed NON-STATIC general relativistic models of the universe with the cosmological constant Lambda set to zero, but otherwise following Einstein's original assumptions which we discussed above in section Einstein, General Relativity, and the Einstein Universe (see also No-524--527): i.e., the cosmological principle and the representation of the mass-energy of the universe by a homogeneous, isotropic, pressureless perfect fluid.

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Caption: Alexander Alexandrovich Friedmann (1888--1925): Russian mathematician, cosmologist, and meteorologist.

Starting from the Einstein field equations of general relativity, Friedmann derived the special equation of motion that describe the behavior of a homogeneous, isotropic universe consisting of a pressureless perfect fluid.

These equations of motion are now called the Friedmann equations were derived in 1922.

In 1924, Friedmann developed some of the models based on the Friedmann equations that we call the collectively the Friedmann models or the Friedmann-Lemaitre models.

The Friedmann models predicted the expansion of the universe and Hubble's law---which Edwin Hubble (1889--1953) discovered observationally in 1929.

Georges Lemaitre (1894--1966) independently rediscovered Friedmann's results in 1927.

Credit/Permission: Unknown Russian photographer, circa or before 1925 / Public domain

Image linked to Wikipedia.

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Because the cosmological constant Lambda was set to zero, the Friedmann-Lemaitre models are pure GR models.

Only gravity and the inertia of the mass-energy determine the universal motion.

In these models, the universe begins from a singularity of infinite density. The singularity was once called the POINT ORIGIN (Bo-85,181), but nowadays people are more likely to call it just the singularity or the Big Bang singularity.

The term Big Bang was first used derisively by Fred Hoyle (1915--2000) in a BBC radio program in 1950 (No-532)---the British have dirty minds, you know.

Hoyle was a co-inventor of the Steady State Universe (Bo-140ff,152ff) which was a serious rival of Big Bang cosmology up to the early 1960s.

The Steady State Universe was an good theory in many ways---a theory doesn't have to be right to be a good theory.

It had falsifiability in the sense used by philosopher Karl Popper (1902--1994)---and it was falsified.

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Caption: "Some observatory buildings at the Institute of Astronomy, Cambridge of the University of Cambridge. The Northumberland Telescope is in the dome on the left. The covered structures in the foreground are mounts for portable telescopes.".

Fred Hoyle (1915--2000) worked for many years at the Institute of Astronomy, Cambridge.

Hoyle is famous for many things---among other things the now discarded, but very intriguing, Steady State Universe.

He also wrote science fiction of which the most noted piece is the The Black Cloud (1957).

Credit/Permission: © User:Cmglee, circa or before 2011 / Creative Commons CC BY-SA 3.0.

Image linked to Wikipedia.

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In modern Big Bang cosmology, the term Big Bang nowadays is generally take to mean the short time period after the singularity in which the light elements of the universe (hydrogen, deuterium, helium, and lithium) are believed to have been synthesized.
Actually, as aforementioned, I think most modern cosmologists do not think the singularity existed.

The singularity is the time zero of the Friedmann-Lemaitre models.

But modern cosmologist think that extrapolating the Friedmann-Lemaitre models back to time zero pushes them beyond where they can be valid.

Quantum gravity and perhaps other effects must supercede general relativity as infinite density is approached.

The singularity is thus thought of as time zero of the Friedmann-Lemaitre models that is approached, but not reached.

The time of the singularity is still used as fiducial time zero of cosmic time with the understanding that it probably never happened.

So the singularity didn't probably set off the Big Bang.

What set off the Big Bang is the 64 dollar question.

How big is the singularity in its theoretical context of taking the Friedmann-Lemaitre models as exactly true? Well if the universe is infinite, it's infinite. Well if the universe if finite, it's a point.

But taking the Friedmann-Lemaitre models as exactly true at the singularity is probably pushing them beyond their validity. Infinities in physics usually mean that you have pushed a theory beyond its realm of validity. That seems likely to the case for Friedmann-Lemaitre models at the singularity.

We should emphasize that the Big Bang is NOT a pressure explosion, but an initial condition of the models (CL-36).

In Big Bang theory, the Friedmann-Lemaitre models start with initial expansion of the universe that is DECELERATED at all times by the mutual gravity of the mass-energy of the universe.

The fate of these models is determined by the density parameter which (as mentioned above) is given the symbol the capital Greek letter Ω and which is often just referred to as Omega.

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Caption: "Uppercase and lowercase Greek letter omega, the 24th letter of the Greek alphabet. Times New Roman font."

The capital omega (which is on the left in the image) is the symbol used for the density parameter in cosmology.

Credit/Permission: Derrick Coetzee (AKA User:Dcoetzee), User:F l a n k e r, 2006 / Public domain.

Image linked to Wikipedia.

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Omega is the ratio of the universal mean mass-energy density ρ to a critical density ρ_crit (of mass-energy) which is a natural TIME-DEPENDENT parameter of the models.

    The critical density is given by

    &rho_crit; =  3H**2    =  9.20451*10**(-27) kg/m**3 * h_70**2  ,  where
                 ________
                 8*π*G

      H=70*h_70 km/s/Mpc is the 
         Hubble constant,
      h_70=(H/70 km/s/Mpc) is the reduced fiducial 
         Hubble constant,
      G=6.67384(80)*10**(-11) is the gravitational constant
      (FK-646).

   Note the present-day critical density 
     is a very small value. 
     For comparison, the density of water is 1000 kg/m**3 recall.

   The density parameter Omega 
   is given by

     Ω  =  ρ/ρ_crit 

   where Omega, 
     density, and critical density are all time dependent, but
     Omega 

         if greater than 1, stays greater than 1 for all time,
         if less than 1, stays less than 1 for all time,
         if exactly 1, stays exactly 1 for all time,

    in pure Friedmann-Lemaitre models
    with Λ=0.

Omega (which is a sort of unitless density) decides the geometry of space and---if the models can be extended to all space---whether the universe is finite or infinite.

Remember in GR, mass-energy determines the geometry of spacetime and spacetime tells mass-energy how to move.

By the by, many people do NOT believe that the models can be extended to all space, and if they are right, whether the universe is finite or infinite is NOT decided by Omega.

These people believe the models can only be extended to our universe domain.

2-dimensional space analogs of possible geometries of space in simple GR models of the universe.

The evolution of the Friedmann-Lemaitre models can be represented compactly by the time evolution of the cosmic scale factor a(t), where cosmic time.

All cosmological physical distances scale with a(t). The cosmological physical distance between any two points at any cosmic time is given by

      r(t)=a(t)*x  ,

                     where x is comoving distance
                     which is a TIME-INDEPENDENT
                     "distance" between the two points. 

The scale factor a(t) does not have to be assigned any specific length itself for many purposes.

However, the common choice is to set a(t=present)=1. Which makes a lot of sense: "our era in the expansion of the universe is the measure of all things" (Protagoras (c. 490--c. 420 BCE), apocryphal).

So for cosmic time past a(t)<1 and for cosmic time future a(t)>1 and

The comoving distances of the present are exactly equal to the present cosmological physical distances

Of course, recall as we look farther out in space, we look further back in cosmic time.

Actually a(t) can be assigned a specific value that has geometrical significance in non-flat spaces (CL-11,12). But we won't worry about that.

The scaling factor a(t) gives the relative scaling up of the universe.

cosmic scale factor a(t)

A diagram illustrates how a(t), and thus how the expansion of the expanding universe, evolves with cosmic time in the three qualitatively distinct versions of the Friedmann-Lemaitre models.

Friedmann-Lemaitre models.

The slope of the curves in the diagram is the rate of change of of a(t): i.e., recession velocity of distance a(t). Since the slope always decreases with cosmic time the expansion continuously decelerates for the Friedmann-Lemaitre models.

The Ω<1 and Ω=1 versions expand forever (although always at a decreasing rate because of the deceleration) and the universe (or our universe domain) will end in the Big Chill (AKA heat death of the universe) which we will discuss below in the section The Fate of the Universe According to the Concordance Model.

If Ω>1, then the universe (or universe domain) will eventually recollapse and there will be a Big Crunch. Since the Big Crunch is itself a singularity, we don't really know what happens then or later.

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Caption: "Section d'univers subissant le Big Crunch."

This is animation can't be taken very literally---it just gives a cartoon of the Big Crunch, I'd say.

Credit/Permission: User:Rogilbert, Public domain.

Image linked to Wikipedia.

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Some have imagined an cyclic universe where the Big Crunch is the Big Bang of a subsequent epoch.

This idea as originally suggested has not lasted, but in the guise of the ekpyrotic universe it has made a bit of a comeback. We briefly discuss the ekpyrotic universe in the section Inflation and Inflation Cosmology.

A KEY POINT is that the Friedmann-Lemaitre models predict either an expansion or a contraction of the universe: i.e., a(t) is never constant, but always changing.

And this was done before Hubble observationally discovered Hubble's law and Hubble was aware of the prediction???. It is hard not to believe that it guided his thinking (No-524).

Hubble's original data was pretty noisy and without the prediction of the expansion of the universe described by the scale factor a(t), he may not have confidence to draw his conclusions about the expansion of the universe and Hubble's law.

At least not as quickly or as confidently as he did.

Hubble's law itself is a consequence of the Friedmann-Lemaitre models. Lemaitre published Hubble's law (based on his models) in French (in the pretty obscure Annals of the Scientific Society of Brussels) in 1927 with a Hubble constant of 625 km/s/Mpc from data he had available (Livio 2011). His value wasn't much worse than Hubble's own value of 500 km/s/Mpc of 1929 (Tamann 2005).

It seems impossible to know if Hubble was aware of Lemaitre's priority on this particular point---Hubble was certainly aware of the prediction of the expansion of the universe. Lemaitre never made any explicit claim for priority (see also No-524--526).

The theoretical Hubble's law of the Friedmann-Lemaitre models is exact for recession velocities and cosmological physical distances measured at one instant in cosmic time.

But the observational law agrees with the theoretical law for cosmologically short distances or cosmologically short lookback times as we have already noted above.

Also, as we mentioned above, the cosmological redshift due to the universal expansion is not actually a Doppler shift (FK-636--637).

Doppler shift are caused by relative motions.

The cosmological redshift is caused by space expanding under the light as it propagates through expanding space.

The formulas for the two kinds of spectral shift are different, but they agree to 1st order in low velocity and thus many books loosely speak of the cosmological redshift as a Doppler shift.

The Friedmann-Lemaitre models in themselves do NOT tells us everything. In particular they do NOT tell us the value of the Hubble constant or of Omega. So they are certainly incomplete cosmological models.

In principle, the Hubble constant and Omega can be determined by observations, of course. In fact, they have been so determined to some accuracy.

How the Hubble constant is determined we have already discussed. How Omega is determined we will briefly mention below in the section The Accelerating Universe and the Friedmann-Lemaitre-Lambda Models.

But the fact that the Friedmann-Lemaitre models predicted the expansion of the universe and Hubble's law before they were discovered is very impressive.

The prediction certainly did suggest that they were right as far as they went.

Question: Which version of the Friedmann-Lemaitre models corresponds to the actual universe (or universe domain)?
1. The Ω > 1, hyperspherical model.
2. The Ω = 1, flat model
3. The Ω < 1, hyperbolical model.
4. None of them.












Answer 4 is right according to the best modern observations.

All the Friedmann-Lemaitre models are decelerating at all times after the Big-Bang singularity.

There is good evidence now that the expansion of the observable universe is accelerating.

The accelerating universe is the subject of the next section The Accelerating Universe and the Friedmann-Lemaitre-Lambda Models

But our discussion of the Friedmann-Lemaitre models has not been a waste of time as we will also see in the next section.

Georges Lemaitre (1894--1966) videos:
1. Georges Lemaitre y la teoria del Big Bang Great---and in Spanish.
2. Au-dela du Big Bang4 Mostly about the Steady State Universe and its battle with the Big Bang theory. Too long and in French.

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The Accelerating Universe and the Friedmann-Lemaitre-Lambda Models

---

How we got where we are now in modern cosmology with lots of omissions:

1. 1917: The static, hyperspherical Einstein universe with non-zero cosmological constant Lambda which was invented to make the universe static (No-520; Bo-97).

2. 1917: The de Sitter universe developed by Willem de Sitter (1872--1934) (No-518,521; CL-28--29,159). This is zero-density, exponentially expanding universe.

   
             a(t) = a_0 exp(t/t_0) , where
   
                 exp is exponential function:  e=2.71828...
                 raised to the power t/t_0,
   
                 a_0 is some fiducial scale distance,
      
                 and
   
                 t_0 is some fiducial cosmic time.
   
                 The exponential function is not at all
                 esoteric:  it describes the growth of
                 a bank account with compound interest---though such accounts don't exist anymore---
                 and uncontrolled population growth.
   
                 Whenever you have growth of an amount proportional to the size of the amount,
                 you have exponential growth.
   
    
           

   Historically, the de Sitter universe is of interest because it was the first model to predict expansion, but, of course, it wasn't right because it had no mass-energy. But nowadays it has been revived as a component of inflation cosmology which has an exponential growth phase.

   We discuss inflation cosmology below in the section Inflation and Inflation Cosmology.

3. 1917 to Mid-1960s: Various universe models including Friedmann-Lemaitre models had vogues for periods of time.

4. Mid-1960s to 1998: In this period Friedmann-Lemaitre models which were the standard cosmological models. They predicted the expansion of the universe and their early dense phase allowed for the constituents of the observable universe to develop. The latter is a subject discuss below in the section Big Bang Cosmology and the Constituents of Observable Universe.

5. 1998 on: In 1998 the first evidence appeared that the universal expansion was accelerating: to be more exact, positively accelerating unlike the Friedmann-Lemaitre models where the expansion is always negatively accelerating (i.e., decelerating).

The acceleration was first discovered by studying Type Ia supernovae.

These are very bright objects that can be seen using the modern giant telescopes to beyond 2500 Mpc (FK-649). Recall the current value for the Hubble length is 4283 Mpc / h_70, and so Type Ia supernovae can be seen to cosmologically large distances.

Their maximum luminosities are known reasonably well, and thus one can determine their luminosity distances from the inverse-square law for light: luminosity distances are not the same as proper distances (except in a static universe), but they can be MEASURED.

 
                        L
           Recall F=___________
                     4*π*r**2

           implies

           r = sqrt[ L/(4*π*F) ] .

           But this calculation neglects the expansion of space during
           the photon flight time and assumes flat geometry.

           Consequently, the distance r so determined is a funny distance
           that we call luminosity distance.  

           It can be used, nonetheless, to determine cosmological 
           parameters in a way we will NOT go into. 

    

The cosmological redshifts of the parent galaxies of the Type Ia supernovae can be measured too.

Thus, one can determine a Hubble diagram for Type Ia supernovae.

Such diagrams extend to great distances with pretty high accuracy, and thus allowed a more sensitive test of Hubble's law and the nature of the expansion of the universe than before.

A schematic Hubble diagram.

The 1998 Hubble diagram for Type Ia supernovae showed deviations from Hubble's law that could reasonably be fitted only if an acceleration of the expansion were assumed.

The deviations were NOT caused by peculiar velocities.

They are caused by the fact that redshift velocities and luminosity distances are not recession velocities and cosmological physical distances in general.

Redshift velocities and luminosity distances only approximate those quantities for the local universe.

Hubble's law is exact for recession velocities and cosmological physical distances in the Friedmann-Lemaitre models as aforementioned.

When the acceleration was first announced, people were somewhat skeptical. The data had a lot of random UNCERTAINTY---the deviations in plots from deceleration looked like pretty much like noise to my eye---and there could have been many systematic errors.

But since 1998, the data for Type Ia supernovae has continued to firm up and in addition 2 other independent evidences for acceleration have appeared.

To summarize without giving any details about how one knows:

1. The Type Ia supernova Hubble diagram directly points to acceleration.

2. Analysis of the cosmic microwave background radiation (CMB) (which we discuss below in the section Big Bang Cosmology and the Constituents of Observable Universe) strongly suggests that Omega=1.00+/-0.02, but gravitational mass in galaxy clusters indicates Omega_matter=0.27+/-0.04 (FK-650,653).

   The missing mass-energy can be interpreted as some kind of dark energy that is powering the acceleration.

3. The integrated Sachs-Wolfe effect (CL-375) (which we won't go into) also points to acceleration.

So acceleration is rather well established: it still might be proven non-existent, but that would take a lot of counter-evidence now.
And if it was disproven would they have to take away the 2011 Nobel Prize in Physics for discovering the accelerating universe from my old pals?

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Caption: "Shaw Prize Astronomy 2006."

Here we see left to right, Saul Perlmutter (1959--), Adam Riess (1969--), and Brian Schmidt (1967--) receiving, NOT the Nobel Prize, but another prize for discovering the accelerating universe. They were, of course, leading members of large groups of people who worked on the discovery.

They did eventually get the 2011 Nobel Prize in Physics.

Credit: User:Ariess (AKA Adam Riess.

Credit/Permission: Adam Riess (AKA User:Ariess), 2006 / Public domain.

Image linked to Wikipedia.

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2011 Nobel Prize in Physics videos:
1. 2011 Nobel Prize: Dark Energy feat. Sean Carroll Sean Carroll (1966--) is another old pal from days at Harvard College Observatory. Too dull for the classroom.
2. Physics Nobel Prize 2011 - Brian Schmidt Brian Schmidt (1967--) on the accelerating universe. Too long for the classroom.
3. Hopkins Professor Earns Nobel Prize In Physics Adam Riess (1969--) in the news for his prize. Too long for the classroom.

How does one accommodate the acceleration theoretically?

Well the possibilities are quasi-endless.

But the simplest way is to fetch Einstein's cosmological constant Lambda back from the storeroom of discarded theories and put it back in the Einstein field equations , but now tune it to give the measured acceleration instead of a static Einstein universe.

One can then derive what one can call Friedmann-Lemaitre-Lambda models which are just the Friedmann-Lemaitre models with the cosmological constant Lambda as an extra free parameter: i.e., an extra controlling variable whose value is not determined by the model and must be determined by observational or other means.

The cosmic scale factor a(t) for an appropriate Friedmann-Lemaitre-Lambda model evolves schematically as in the following diagram.

Accelerating universe based on CM-455.

The increasing slope of the accelerating a(t) curve is the signature of acceleration.

Note that the accelerating model starts in a decelerating phase and then makes a transition to acceleration about 5 Gyr ago.

The transition to acceleration is less certain than the acceleration itself, but recent data for Type Ia supernovae suggest it (FK-650--651).

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Dark Energy

---

The acceleration of the universe in the Friedmann-Lemaitre-Lambda models is simply turned on by setting the cosmological constant Lambda to a sufficiently large positive value (CM-454).

But what does Lambda mean physically?

In the Einstein field equations, Lambda just appears as a modification to how gravity affects spacetime. It is a ``just-so'' modification.

In modern physics, there is a strong preference to interpret Lambda as representing a NEGATIVE PRESSURE (GR-277--278) which has an associated energy. We call this energy dark energy because we don't see it so far in any other way than through its effect on the universal expansion.

The NEGATIVE PRESSURE itself causes an inward sucking instead of an outward push like ordinary pressure. But this pressure effect is weak and cancels completely if the NEGATIVE PRESSURE is uniform in space which is the case when assuming it is governed by the cosmological constant (GR-520).

What is not canceled is the cumulative effect of the gravity of dark energy which becomes stronger over larger separations (GR-279). And this gravity effect is REPULSIVE---anti-gravity of a sort at last it seems---but people don't call it anti-gravity (GR-278).

Einstein used the REPULSIVE GRAVITY---a very ugly kind of gravity---to exactly counter ordinary gravity and make the static Einstein universe. But the cosmological constant can be turned up to drive the acceleration of the universe.

Now cosmological-constant dark energy has a constant energy density in time and space. It is about the simplest kind of dark energy imaginable.

That the cosmological-constant dark energy density is constant in time is UNUSUAL. For example, matter density must decrease because of the expansion of the universe. In fact, as cosmic scale factor a(t) increases, volumes increase by a(t)**3, and matter density falls as a(t)**(-3).

The cosmological-constant dark energy density can be treated as a contribution to Omega: we denote this contribution by Omega_Lambda.

Question: Omega is:
1. the cosmological constant by an other name.
2. the last letter of the Greek alphabet.
3. the ratio of the mass-energy density of the universe (or our universe domain) to the critical mass-energy density. It is the parameter that determines the geometry of space in the Friedmann-Lemaitre models and the Friedmann-Lemaitre-Lambda models.











Answer 2 and 3 are right. But answer 3 is best in this context.

From the analysis of the CMB data, galaxy cluster data, and Type Ia supernovae ASSUMING the dark energy is a cosmological-constant dark energy, one finds Omega_Lambda=0.73+/-0.04 (FK-653).

But the dark energy need not have constant density in either time or space and it may interact with other forms of mass-energy in ways we do not know.

So far nothing in the observations tells us to go beyond the simple theory of cosmological-constant dark energy.

But it would NOT be surprising if eventually we had to.

Is there any reason for believing there could be just cosmological-constant dark energy from physical theory?

Yes, quantum field theory (i.e., relativistic quantum mechanics) suggests there could be cosmological-constant dark energy, but alas predicts its density to be 10**120 times bigger than needed to fit the observed acceleration (e.g., Carroll, S. 2003, p. 3, Why is the Universe Accelerating?).

This remarkable OVERESTIMATE suggests that the dark energy is more complex than the simple cosmological-constant dark energy with a density which is constant in time and space.

It is also strange that the cosmological-constant dark energy density from the analysis of the CMB data is Omega_Lambda=0.73+/-0.04, which is COMPARABLE to the matter density Omega_matter=0.27+/-0.04 (FK-653).

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Caption: ESTIMATED distribution of universe mass. Dark energy makes up 74 % and dark matter makes up 22%. Ordinary matter making up only 4% of the mass of the universe. And most of this ordinary matter is nearly invisible intergalactic medium (IGM) (hot hydrogen gas): i.e., it is ordinary dark matter.

This distribution is that of the concordance model.

Credit/Permission: NASA, circa or before 2007 / Public domain.

Image linked to Wikipedia.

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There may be some deep reason why the dark energy and matter should be connected in which case the dark energy CANNOT be simply a cosmological-constant dark energy.

Possibly the COMPARABILITY of Omega_Lambda=0.73+/-0.04, and matter density Omega_matter=0.27+/-0.04 is explained by the anthropic principle.

Say there are an infinity or a quasi-infinity of universe domains in the multiverse with different parameters set by some probability distribution of parameters.

Those somewhat like our own universe domain may NOT be able to support life if there was no COMPARABILITY.

Too small a cosmological-constant dark energy density and the universe may not have formed the right kind of galaxies and stars.

Too large a cosmological-constant dark energy density and the universe would have expanded too quickly ever to form galaxies and stars.

It is very hard to prove an argument based on the anthropic principle.

But such an argument could be falsified if the dark energy density and matter density were fine-tuned beyond the needs (so far as we can tell) of making the universe domain suitable for us to be here.

For example, the ratio is now of dark energy density to matter density is approximately 3 to 1.

If the ratio were exactly 3 to 1, then that is more exactness than is needed for a universe domain approximately like ours that can support life like us, and strongly suggests a deep connection between dark energy and matter---not just that random throw of the parameter dice.

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The Concordance Model

---

Assuming that the Friedmann-Lemaitre-Lambda model is correct, one adjusts its free parameters to fit the modern data from Type Ia supernovae, the CMB (which we will discuss below in the section Big Bang Cosmology and the Constituents of Observable Universe), and galaxy cluster observations.

The resulting model is called the concordance model or the Lambda-CDM model (where CDM stands for cold dark matter).

CDM stands for cold dark matter. It's dark matter which is slow-moving.

Cold dark matter has been favored since the 1980s for being the kind of dark matter needed to explain the large-scale structure of the universe.

______________________________________________________________________________

Concordance Model Parameters
________________________________________________________________________________

Quantity               Value                    Short explanation

________________________________________________________________________________

Hubble constant H      71(+4/-3) (km/s)/Mpc     present day expansion rate

Hubble time 1/H        13.8 Gyr                 characteristic universe age 

Age of universe        13.7+/-0.2 Gyr           time since the big bang

Hubble length c/H      4234 Mpc                 characteristic radius of 
                                                  the observable universe

Particle horizon       14000 Mpc 

Age of universe        379,000+/-8,000 years    time when the protons 
  at recombination                                
                                                  and electrons combined
                                                  to make neutral hydrogen 

Ω                      1.02+/-0.02              total of all mass-energy density
 (density parameter)                              of universe divided by
                                                  critical density.
                                                  Omega determines the geometry
                                                  of space.

Ω_dark_energy          0.73+/-0.04              dark energy contribution

Ω_exotic               0.23+/-0.04              exotic dark matter 

Ω_ordinary_matter      0.044+/-0.04             ordinary matter:  dark and
                                                  luminous 

Ω_luminous             0.007                    luminous matter:  stars,
                                                  H I gas, H_2 gas,
                                                  hot H II gas in X-ray galaxy 
                                                  clusters. 

________________________________________________________________________________

References:
1. Wikipedia: Concordance model: Parameters
2. FK-653
3. Davis, T. M., & Lineweaver, C. H. 2003, Publications of the Astronomical Society of Australia, astro-ph/0310808, Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe
4. Spergel, D. N. et al. 2003, ApJ, astro-ph/0302209, First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
5. Cen, R., & Ostriker, J. P. 1999, ApJ, 514, 1, astro-ph/980628, Where are the Baryons?
6. Fields, B. D., & Sarkar, S. 2003, astro-ph/0406663, Big Bang Nucleosynthesis in The Review of Particle Properties (2004)

         
________________________________________________________________________________

Some comments about the concordance model are in order:

1. The many of the observations have gone into determining concordance model parameters are thought to be very accurate. But the uncertainties could be larger than is thought.

2. If the Friedmann-Lemaitre-Lambda models (of which the concordance model is a special case) are essentially wrong then derived quantities like the age of the universe and Omega might be wrong.

   If a model is wrong, then observations need to be interpreted in a different way.

3. And the concordance model may indeed be wrong. As we have discussed above a cosmological-constant dark energy is the simplest theory of the acceleration---and so far this theory is adequate to explain the observations.

   But future observations, particularly of the past history of the universal expansion using Type Ia supernovae, may show that cosmological-constant dark energy is wrong.

   This would NOT be surprising.

   The simplest adequate theory is often the first theory one should investigate---crawl before running---but astronomers are always finding things more complicated than they first thought---it's sort of expected.

4. The exotic dark matter may well be some strange, new particle that interacts weakly with matter, except through gravity: a WIMP (weakly interacting massive particles).

   There are many ideas about what WIMPs are and some tentative claims of possible detections of something in the laboratory or astronomically, but the possibilities are still wide open.

   The requirement for exotic dark matter is an inference as we will explain right now.

   Big Bang nucleosynthesis (which discuss below the section Big Bang Cosmology and the Constituents of Observable Universe) predicts Omega_ordinary_matter equal to about 0.044, and velocity studies of galaxies and galaxy clusters demand Omega_matter at about 0.27+/-0.04.

   Big Bang nucleosynthesis is itself a very robust theory, and so we are forced to believe exotic dark matter is likely.

   If we ever discover exotic dark matter, it will have profound implications for cosmology and fundamental physics.

   Note if MOND (MOdified Newtonian Dynamics turns out to be at all right, then the need for exotic dark matter may vanish and all of cosmology would be affected in radical ways.

   In the worst of all possible worlds, MOND is right, but we still have dark matter particles.

5. Most of the ordinary matter is dark and we call it ordinary dark matter.

   ordinary dark matter is either included in dark matter or its not. Context must decide what is meant.

   From Big Bang nucleosynthesis, Omega_ordinary_matter equal to about 0.044.

   But adding up all the luminous matter gives only 0.007 (e.g., Cen, R., & Ostriker, J. P. 1999, ApJ, 514, 1, astro-ph/980628, Where are the Baryons?).

   ordinary dark matter is about 5 to 10 times more abundant than luminous matter.

   ---

   

   Caption: ESTIMATED distribution of universe mass. Dark energy makes up 74 % and dark matter makes up 22%. Ordinary matter making up only 4% of the mass of the universe. And most of this ordinary matter is nearly invisible intergalactic gas (hydrogen and helium gas): i.e., it is ordinary dark matter.

   This distribution is that of the concordance model.

   Credit: NASA.

   Image linked to Wikipedia.

   Permission: Public domain at least in USA.

   ---

   Some of this ordinary dark matter may be in the form of brown dwarfs (star-like objects too small to burn hydrogen), dim white dwarfs, dim neutron stars, and black holes.

   ---

   

   Caption: Relative sizes of the Sun and Jupiter and estimated relative sizes of red dwarf star Gliese 229A and brown dwarfs Gliese 229B and Teide 1 (which was the first verified brown dwarf (1995)).

   Credit: User:Bryan Derksen and NASA.

   Permission: Public domain at least in USA.

   Image linked to Wikipedia.

   ---

   But perhaps not much of it. The idea that MACHOs (Massive Compact Halo Objects) (brown dwarfs, dim white dwarfs, dim neutron stars, and black holes) may make up a lot of the ordinary dark matter is at present disfavored.

   Re-analysis of the MACHO data suggests there may be few or almost no MACHOs (e.g., Evans, N. W. & Belokurov V. 2004, astro-ph/0411222, RIP: The MACHO Era [1974--2004]). But the issue is very controversial right now.

   So what is the ordinary dark matter?

   At present, the favored idea seems to be that it is the diffuse nearly invisible intergalactic medium (IGM) (hydrogen and helium gas). makes up most or maybe almost all of the ordinary dark matter (e.g., Cen, R., & Ostriker, J. P. 1999, ApJ, 514, 1, astro-ph/980628, Where are the Baryons? [hereafter CO], CO-3). Much of this gas hot. The idea is that it falls in from voids and gravitational potential energy gets converted to heat energy. The gas is then the warm-hot intergalactic medium (WHIM) (i.e., ionized H and He gas with temperatures in range 10**5--10**7 K) and along with slightly warmer and colder gas. Shocks from galaxy collisions and outflows from active galaxies give more heating. Some heat energy may be left from the original phase of galaxy formation. WHIM cools very slowly.

   WHIM is almost invisible because it emits low energy X-rays (which are mostly drowned out by Milky Way X-ray emission) and extreme ultraviolet light to which the neutral Milky Way hydrogen is opaque (CO-3).

   We have found some WHIM, but it not yet quite clear??? that WHIM is most of the ordinary dark matter.

   Eventually, maybe in several Hubble times, some of the WHIM will be cooled enough to collapse into new galaxies (CO-5). This would keep star formation going in the universe for some time. But the continued and accelerated expansion of the universe might prevent all of it from collapsing????.

---

The Fate of the Universe According to the Concordance Model

---

---



Caption: "U.S stamp with the picture of the poet Robert Frost (1874--1963). Date 1974 March 26.

Fire and Ice

Some say the world will end in fire,
Some say in ice.
From what I've tasted of desire
I hold with those who favor fire.
But if it had to perish twice,
I think I know enough of hate
To know that for destruction ice
Is also great
And would suffice.


Robert Frost (1874--1963). First published 1923. Reference site: Representative Poetry Online, Department of English, University of Toronto.

Credit: US Federal Government

Image linked to Wikipedia.

Permission: Public domain at least in USA.

---

What is the fate of the universe (or our universe domain) if the concordance model is taken as absolutely correct?

Well a highly speculative sketch---which gets more speculative as it goes along---is as follows (HI-477):

1. Current, cosmic time is 13.8*10**9 years = approximately 10**10 years.

2. At cosmic time of order 10**13 years (about 1000 times the current cosmic time), all star formation will have ended and the universe will consist of mainly of exotic dark matter (probably), compact remnants (i.e., white dwarfs, neutron stars, and black holes), and, perhaps, some uncollapsable H and He gas.

3. It is possible that protons decay (and this entails the decay of neutrons too) into electrons, positrons, neutrinos, and photons with a half-life of something in excess of 10**32 years. Thus on some cosmic time in excess of 10**32 years, the protons and neutrons will have all decayed. This will leave a dilute gas of electrons, positrons, neutrinos, and photons, and exotic dark matter particles, and black holes.

4. Black holes are theorized to evaporate by Hawking radiation.

   By a cosmic time of order 10**100 years, the black holes may have evaporated and the vastly expanded universe could be only a very dim, dilute gas of electrons, positrons, neutrinos, and photons, and maybe exotic dark matter particles.

   This is the end of the story---but there's no reason to put much faith in it---it's a very speculative story.

---

Big Bang Cosmology and the Constituents of the Observable Universe

---

Now the Friedmann-Lemaitre-Lambda models are big bang models in the sense that they begin from the Big-Bang singularity, and so we've been discussing Big Bang cosmology for some time.

But Big Bang cosmology is more than the Friedmann-Lemaitre-Lambda models.

It is also an explanation and history of the constituents of the universe (or of our universe domain at least) beginning from an early hot, dense phase of the universe which is the primary meaning of the term Big Bang in modern cosmology.

We are going beyond the perfect fluid picture for the matter in the universe that the simple Friedmann-Lemaitre-Lambda models assume.

The ancestor of the Big Bang theory for the constituents was Georges Lemaitre's (1894--1966) primeval atom theory---but we won't discuss that historically interesting, but long discarded, theory. (No-530).

Georges Lemaitre (1894--1966).

In the 1940s (by which time nuclear physics was somewhat elucidated), George Gamow (1904-1968), Ralph Alpher (1921--2007), and Robert Hermann (1914--1997) worked out an early version of Big Bang nucleosynthesis (No-531ff, 559ff): the theory that the elements were synthesized by nuclear fusion from hydrogen nuclei in an early hot, dense phase of the universal expansion: i.e., in the Big Bang in the primary meaning of the term.

---



Caption: George Gamow (1904-1968) was born in Russia. He was briefly a colonel---his rank was assigned on the basis of his academic status---in the Red Army---in the cavalry---he rode a pony. But later defected to the USA---and become the primary discoverer of the Big Bang theory.

Credit/Permission: Unknown photographer before 1950, I'd guess, (uploaded to Wikipedia by Serge Lachinov 2010 / Public domain.

Image linked to Wikipedia.

---

Originally, Gamow et al. tried to show that all the nuclei could have been formed in this early phase (Bo-58), but later this turned out to be impossible it seems (No-560). The heavier nuclei are accounted for by nucleosynthesis in stars followed by ejection by stellar winds and supernovae (No-540).

But stars cannot account for certain light elements: hydrogen (H-1), deuterium (H-2), helium (He-4 and He-3), and lithium (Li-7 and Li-6) (see Wikipedia: Big Bang nucleosynthesis).

The case for He is particularly acute: there seems too much to have been produced in stars.

Recall the universal abundances by mass are about the same as the solar composition 71 % H, 27 % He, and 2 % metals: these numbers, in particular the last one, vary a bit from reference to reference (e.g., Cox-28).

The light elements can be accounted for by Big Bang nucleosynthesis.

The idea is to start cosmic time at some early hot, dense phase of the universe with some simple primordial constituents and then run the clock forward synthesizing the nuclei as space expands and cools. The gas expands with space and this cools it by a commonplace physical effect: adiabatic cooling---which we won't go into, but its everywhere including everyday life.

We can't start the clock at TIME ZERO. At infinite density, our physical concepts break down.

In fact, before about one Planck time (t_Planck = approximately 5*10**(-44) s) our theories are very speculative. This period is called the Planck epoch.

In the Planck epoch the density is so high that quantum effects on gravity must have been important by general quantum mechanical principles even though we don't know what those effects are (CL-122).

So general relativity must fail in the Planck epoch which is a good reason for not believing in the infinite density singularity.

The very earliest times before a second or so are in also in speculative realm (thought not as speculative as the Planck epoch) where the matter is believed to be so hot and dense that only quarks and leptons (the most familiar of which is the electron) and their antiparticles exist and in which matter and antimatter are about equal in abundance (FK-668).

There are probably also exotic dark matter particles about, but what they are doing is uncertain.

Quarks make up protons and neutrons.

Free quarks exist only under super-dense conditions. If you try to pull apart composite particles (e.g., protons) made up of quarks under less dense conditions, new quarks come into existence to make new composite particles.

The energy from the pulling apart goes into making the new composite particles.

Leptons are electrons, positrons (antielectrons), neutrinos, and some less common species.

Matter and antimatter mutually annihilate to produce photons.

The mutual annihilation destroys the antimatter and leaves a trace of matter.

It is thought in theories of particles that there is some asymmetry in properties between matter and antimatter that slightly favors matter (FK-668).

To just give a simple sketch of the early universe a sequence of snapshots is useful.

We assume that the early universe is very homogeneous: i.e., among other things has nearly constant temperature, density, and composition at any given cosmic time. The continuous expansion causes the temperature and density to fall steadily.

There are small density fluctuations that will be the seeds of the large-scale structure that will form in of order the first billion years. Gravitational runaways will start from the seeds.

The times given with the snapshots are subject to revision from time to time and so should be taken a rough values.

The snapshots:

Early universe 1: t= about 10**-35 s.

In this early phase, the strong nuclear, weak nuclear, and electromagnetic forces may have been united: i.e., acted in the same way (FK-664). There may be exotic particles around too. This epoch may have been just before inflation: see just below and FK-661.

Early universe 2: t = about 2 s.

Early universe 3: t = about 3--15 minutes. This is after the famous First Three Minutes.

Early universe 4 (recombination epoch): t = about 380,000 years.

Early universe 5: t = about 1 Gyr.

After snapshot 5, the universe (or universe domain) continues to evolve to our present epoch.

The recombination epoch is when the electrons and nuclei combine to form NEUTRAL ATOMS: mainly hydrogen and helium, of course.

The NEUTRAL ATOMS have much lower cross sections for interactions with photons of the temperature of the recombination epoch of about 3000 K (FK-670).

A cross section in physics is a measure of the probability of interaction of particles during encounters.

The lower cross sections of NEUTRAL ATOMS are such that after about the recombination epoch, the matter in the universe or universe domain becomes largely transparent to the primordial photons after the recombination epoch.

Before the recombination epoch, the photons interacted strongly with matter and thus matter and photons were held a the same temperature. At recombination itself this temperature was about 3000 K as noted above (FK-670). The photons then had a blackbody spectrum of about 3000 K.

After recombination epoch the primordial photons stream off through space only slightly interacting with matter again.

They do interact a little, of course: they can scatter off free electrons in space, run into stars and planet, be affected by gravitational effects, and other lesser interactions.

The primordial photons cool by expansion of the universe. Their wavelengths scale with the cosmic scale factor a(t) and their density decreases as the volumes scale up.

In fact, it can be shown that primordial photon distribution remains blackbody-like with a constantly decreasing temperature due to expansion.

In 1949, Alpher and Hermann predicted the present-day temperature of the primordial photons would be about 5 K. (No-559).

Using Wien's law

                   2900 micron-K
     lambda_peak = _____________  = about 600 microns = 0.06 cm  
                        5 K

which by common definition is long wavelength infrared (HZ-54; FK-94). But the microwave band is redward of 0.1 cm where much of the primordial photon spectrum is.

Thus, this relic primordial photon gas is called the cosmic microwave background radiation (CMB).

In 1965, Arno Penzias (1933--) and Robert Wilson (1936--) working with a Bell Laboratories radio telescope in Holmdel, New Jersey fortuitously discovered the CMB at 7.3 cm: a nearly uniform radiation from all directions (No-561ff).

---



Caption: Arno Penzias (1933--) (right) and Robert Wilson (1936--) (left) with the radio antenna in Holmdel Township, New Jersay where in 1965 they discovered the cosmic microwave background radiation (CMB).

Penzias and Robert Wilson received 1978 Nobel Prize in Physics for their discovery;

It is de rigueur in this context to mention that to be sure that they weren't just detecting instrumental noise, they had to clean history's most famous pigeon guano out of their antenna.

Credit/Permission: National Park Service, probably before 2000 / Public domain.

Image linked to Wikipedia.

---

Penzias and Wilson got the 1978 Nobel Prize in Physics for their discovery; Alpher and Hermann did NOT get a Nobel Prize.

A Swedish friend once commented to me: ``The question is not why the Swedes decide the Nobel Prize; the question is how do they decide the Nobel Prize.'' Apparently, it's a mystery even in Sweden.

The CMB is best measured from space, because the Earth's atmosphere is opaque to much of the spectrum of the CMB.

The first highly accurate CMB measurement over a broad wavelength range was reported from the COBE probe circa 1990 (FK-640).

---

Cosmic microwave background radiation (CMB) from COBE and other detectors.

The plot is logarithmic on all three axes.

The microwave band by one convention is redward of 0.1 cm; blueward is infrared (HZ-54).

The data is excellently fit by a blackbody spectrum has a temperature of T=2.726+/-.001 K.

Credit: CMB Astrophysics Research Program: COBE site This is a Lawrence Berkeley Lab site reporting on George Smoot's group.

---

The CMB has a large-scale variation caused by the Earth's peculiar velocity with respect to the local inertial frame participating in the mean expansion of the universe (FK-640--641).

Question: The effect that actually causes the large-scale variation is:
1. the cosmological redshift.
2. Doppler shift.
3. the cosmological blueshift.












Answer 2 is right.

There is a slight blueshift in the direction of the Earth's motion and a slight redshift in the opposite direction.

Answer 1 is the reason the CMB has cooled down from 3000 K to about 3 K since the recombination epoch.

The solar system's peculiar velocity with respect to the local inertial frame is, in fact, best known from the large-scale CMB variation.

The motion is 371 km/s in the direction of Leo and away from Aquarius FK-640--641).

We can deduce that the Local Group of galaxies is moving at 620 km/s relative to the mean expansion in the direction the Hydra-Centaurus Supercluster (FK-640--641).

If the large-scale variation is removed, there remain small-scale random fluctuations in CMB temperature of order 200 micro-Kelvins or in relative terms of 1 part in 10**4.

These fluctuations were first measured to low accuracy by the COBE satellite in the early 1990s. People were relieved that that were finally found. They had been expecting them for some time.

Since then the measurements of the fluctuations have been considerably improved particularly by the WMAP satellite that has been active since 2001 (NASA's Wilkinson Microwave Anisotropy Probe (WMAP)).

The CMB temperature fluctuations are believed to correspond to primordial density fluctuations that were the seeds for the gravitational collapses that led to the formation of the galaxies and the large-scale structure (see IAL 28: Galaxies).

---

Cosmic microwave background radiation (CMB) all-sky map from WMAP circa 2003.

Why is there no scale?

The average temperature is 2.725+/-0.001 K.

The colors code deviations in micro-Kelvins: dark blue (-200), green (0), red (+200).

Credit: NASA/WMAP Science Team.

---

To return to the cosmic abundances of the elements and Big Bang nucleosynthesis.

Modern Big Bang nucleosynthesis depends on the parameter the primordial baryon-to-photon ratio η which is of order 10***(-9). The best value is maybe 6.1*10**(-10) (see "Best" Cosmological Parameters, 2003). In this context, the baryons are overwhelmingly just protons and neutrons.

The baryon-to-photon ratio η is an adjustable free PARAMETER of the calculations.

The WMAP measurements of the CMB and observed primordial deuteron abundance actually give a value for this ratio of (6.13+/-0.25)*10**(-10). (Spergel, D. N. et al. 2003, ApJ, astro-ph/0302209, First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters; Mathews, G. J., et al. 2004, Phys. Rev. D, submitted, astro-ph/0408523, Big Bang Nucleosynthesis with a New Neutron Lifetime).

With the ratio parameter set to this value, the predictions of calculations of Big Bang nucleosynthesis can be compared with measured light elements corrected for stellar nucleosynthesis effects where possible.

_____________________________________________________________________________

Big Bang nucleosynthesis (BBN) Predictions and Observed Elemental Abundances
Corrected where Possible for Stellar Nucleosynthesis Effects 
_____________________________________________________________________________

Element        BBN           Observed                   Quantity

_____________________________________________________________________________

He (He-3,4)    0.246          0.245+/-.001              mass fraction
D (H-2)        2.5            2.5 to 3                  D/H * 10**-5  
He-3           1              none available            He-3/H * 10**-5
Li-7           4.5            1.5+/0.5                  Li-7/H * 10**-10
_____________________________________________________________________________

Note: He-3 and He-4 cannot easily be distinguished observationally. They are chemically and spectroscopically nearly identical since they are both isotopes of helium. Reference: Mathews, G. J., et al. 2004, Phys. Rev. D, submitted, astro-ph/0408523 Big Bang Nucleosynthesis with a New Neutron Lifetime

_____________________________________________________________________________

The agreement is actually excellent over 10 orders of magnitude, but remember the deuteron abundance was fitted????.

The Li-7 does not agree within error, but Li-7 can both be created and destroyed in stars and correcting observed abundance to primordial abundance is very uncertain. At the moment, there is no reason to believe this discrepancy is a significant problem.

---

Let us summarize the strongest evidence for Big Bang cosmology:

1. The observed expansion of the universe is predicted. This was done before it was observed.

2. The observed CMB is predicted naturally as the relic of the hot early universe (or our hot early universe domain). This was also done before it was observed.

3. The observed light element abundances are well predicted.
   In 2011, primordial clouds of Big Bang hydrogen and helium gas were discovered. These clouds date from about 2 Gyr after the Big Bang and somehow avoided pollution by metals formed and ejected from early stars.

   The clouds are at cosmological redshift z=3.

   The clouds constituent another verification of the Big Bang theory.

4. The observed large-scale structure can be explained as having been seeded by the primordial density fluctuations that manifest themselves in CMB fluctuations.

   Calculations starting from the primordial fluctuations and using many assumptions especially about the dark matter do seem to be reproducing the observed large-scale structure though a lot of uncertainty remains (FK-671ff).

5. The oldest stars whose age we can well determine by modeling are in Milky Way globular clusters. The modeling is subject to some uncertainties, but has improved greatly since it began in the 1950s. The ages are of order 12.5+/-1.0 Gyr (FK-638).

   These ages are less than the 13.7 Gyr age of the universe concordance model (FK-653).

   At present, there is no problem with contents of the universe being older than the Big Bang cosmology predicted age of the universe which in the past has occasionally been an embarrassment (Bo-39,51--52).

At present, there are no viable, attractive rivals to Big Bang cosmology.

And this has really been so since the the 1960s despite the attempts of mavericks like Fred Hoyle (1915--2000) to present viable alternatives.

The alternatives have always had many ad hoc and/or complicating assumptions.

These assumptions are mostly fix-ups to try to explain things that Big Bang cosmology explains in a natural way.

Big Bang cosmology is a very robust theory nowadays.

It would be astonishing if it turned out to be just plain WRONG.

It is probably right as far as it goes.

But Big Bang cosmology does NOT go everywhere.

1. It has free parameters (e.g., the Hubble constant , Omega, and the baryon to photon ratio) that have to be set by observations. An ideal theory should tell us everything without observational input.

2. It does NOT explain dark matter nor dark energy. Since it doesn't explain dark energy, we do NOT understand the acceleration or how long it will last.

   Perhaps, MOND (MOdified Newtonian Dynamics) will upset things more or clarify things if it turns out to be at all correct.

   Recall MOND requires both Newtonian gravity and general relativity to be modified for low accelerations.

   Such modifications could radically change much of our cosmological theory.

3. It does NOT explain what happened before the Big-Bang singularity if that existed at all, or what happened before the earliest time that we can track backward in time using known physics: i.e., before the end of the Planck epoch????.

4. It does NOT tell us if our universe domain is the whole universe or not.

   Many think it possible that our universe domain is NOT the whole universe.

5. There are what are called the horizon problem and the flatness problem that have no natural explanation in the opinion of many in Big Bang cosmology.

   We will take these problems up just below in the section Inflation and Inflation Cosmology.

---

Inflation and Inflation Cosmology

---

``I could be bounded in a nut shell and count myself a king of infinite space, were it not that I have bad dreams.''

Hamlet, Act II, Scene 2, about 45 % down by William Shakespeare (1564--1616). See MIT's The Complete Works of William Shakespeare.

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Caption: Edwin Booth (1833--1893) as Hamlet.

Credit/Permission: J. Gurney & Son, New York, circa 1870 / Public domain.

Image linked to Wikipedia.

---

The relevance of the quote will emerge below.

Inflation is the name for a super-rapid expansion phase that may have happened in the early universe. The expansion is much more rapid than in the conventional Friedmann-Lemaitre-Lambda models.

After the inflation the cosmic evolution is supposed to track into a Friedmann-Lemaitre-Lambda model or something similar.

The idea of inflation was developed independently by Alexei Starobinsky (1948--) in Russia and Alan Guth (1947--) in the US in 1979. Guth also coined the term inflation (Ov-240,242,245).

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Caption: Alan Guth (1947--) at Trinity College, University of Cambridge, Cambridge, United Kingdom, 2007, December.

Alexei Starobinsky (1948--) of Russia and Alan Guth (1947--) of the US were the first proposers of the inflation cosmology in 1979.

If I recall correctly I was in the same room with Guth for a seminar some time in the interval 1991--1993.

Credit/Permission © Betsy Devine (AKA User:Betsythedevine), 2007 / Creative Commons CC BY-SA 3.0.

Image linked to Wikipedia.

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Since 1979 the concept of inflation has evolved quite a bit and spawned a quasi-infinity of inflation theories.

Inflation was and is considered a good idea just because it offers explanations for three problems.

In science, "problem" often means a perplexing feature of observations or theory that needs to be explained in order to exorcise perplexity.

The three problems are:
1. MAGNETIC MONOPOLE PROBLEM: Guth's original reason for studying inflation was to solve the MAGNETIC MONOPOLE PROBLEM. Magnetic monopoles are isolated magnetic poles: we ordinarily always see magnetic dipoles: there is always and north and south pole.

   The problem is one that PARTICLE PHYSICISTS created for themselves. Grand Unified Theories (GUTs), which unite the strong nuclear, weak nuclear, and electromagnetic forces, seem to predict that MAGNETIC MONOPOLES should be created in the early universe and be as common as protons and be much more massive (Ov-239--240). But none are observed and they havn't caused a rapid recollapse of the universe.

   A phase of inflation would decrease the MAGNETIC MONOPOLE DENSITY to practically unobservable: Guth originally estimated about one MAGNETIC MONOPOLE in the observable universe (Ov-245).

   Problem solved---if it ever really existed.

2. Horizon problem: The temperature of CMB is extremely uniform. It shows fluctuations of only about 1 in 10,000 (FK-645).

   This implies that the whole early universe was very homogeneous and in very nearly in exact thermodynamic equilibrium (i.e., at nearly the same temperature).

   But in Friedmann-Lemaitre-Lambda models, points on opposite sides of sky from which CMB flux originated were never CAUSALLY CONNECTED (except perhaps in a limting sense at that the physically indeterminate Big-Bang singularity itself).

   Those points are NOT within each other's observable universes

   How could the early universe have such a uniform temperature if it never had a chance to thermally equilibrate?

   More generally how could the early universe be so homogeneous?

   This is the horizon problem.

   One could solve the problem by just saying the universe was created ex nihilo with uniform conditions at the Big-Bang singularity or at the Planck time.

   But why then was it not created exactly uniform?

   And anyway physicists do not like to accept at blank wall at the Planck time. They want to know what happened before.

   Inflation solves the horizon problem by saying all the observable universe and more started from a minute region of space that was CAUSALLY-CONNECTED and in thermodynamic equilibrium and inflationary expansion blew it up to sizes that the expansion of Friedmann-Lemaitre-Lambda models could not achieve.

   This solves the horizon problem and also indicates that beyond the region of inflation there are other universe domains.

3. Flatness Problem: The observable universe has Omega very close to 1: the best available measurements give Omega=1.02+/-0.02 for the present epoch (FK-653).

   Friedmann-Lemaitre-Lambda models with Lambda=0, Omega(t) (i.e., Omega as a function of cosmic time) always diverges from 1, unless it is exactly 1. In other words, Omega=1 is an unstable state.

   The divergence of Omega.

   In order to as close to 1 as it is today (i.e., for the universe domain to be as flat as it is today: i.e., with Omega=1.02+/-0.02 [FK-653"]), Omega at the Planck time must satisfy

   
   |Omega(Planck time)-1| = about 10**-60
   
          

   (CL-154).

   The universe must have had Omega fine-tuned to very nearly 1 at early times.

   Perhaps this is just a fundamental initial condition, but as with the horizon problem physicists don't like to that idea.

   They prefer to regard the present day closeness of Omega to 1 as a problem to be solved: i.e., the flatness problem.

   Now the dark energy or non-zero cosmological constant Lambda must complicate the analysis---but no text says the flatness problem goes away.

   Inflation solves the flatness problem by ``stretching'' space flat: this also means the requisite energy density of space for flatness must also be created.

   Inflation predicts that Omega will show some fluctuations in our universe domain that typically it should differ from 1 by about 1 out of 10**5 (CL-155).

   This prediction for Omega was made back in the early 1980s when the observed Omega was only about 0.3. Only since about 2000 has the observed Omega come close to 1.

   It is impressive that inflation predicted the modern result before it was observed.

   It will be interesting to see if the error of the observed Omega can be further reduced and then if the agreement with inflation will still persist.

   But improving the current Omega measurement with its 2 % error will be very difficult.

   One must always recall that Omega is a parameter of the Friedmann-Lemaitre-Lambda models.

   If those models turn out to be essentially wrong, then the observations that lead to our Omega determination may require other interpretations and Omega itself may be somehow meaningless.

So we see inflation offers solutions to three problems that physicists have with the standard Big Bang cosmology.

These solutions are general to most INFLATION MODELS.

A main problem with inflation is that there are tens of different INFLATION MODELS.

Which of any are right is so far beyond us. Some INFLATION MODELS have been ruled out, of course.

All one can say is that the general physics of inflation seems a good idea.

Here I will only vaguely sketch what is called eternal inflation based largely on combination of FK-661--667, Gr-272--323, and Carroll, S., & Chen, J. 2004 Spontaneous Inflation and the Origin of the Arrow of Time (hereafter SC).

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Caption: Andrei Linde (1948--), the main developer of the theory of eternal inflation beginning in 1986.

Credit/Permission: © User:Hypermultiplet, 2012 / Creative Commons CC BY-SA 3.0.

Image linked to Wikipedia.

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Eternal inflation is one of the most popular inflation theories.

I'm going to be vague because as a non-expert, I can't be sure if all my interpretations of the experts are exactly right---but there is enough uncertainty about inflation that anything I say is probably within the bounds of uncertainty.

Eternal inflation posits a background universe that is a high energy vacuum or false vacuum.

Vacuum in modern physics is not passive, empty space, but a seething mess of quantum fluctuations in which VIRTUAL PARTICLES are constantly popping into and out of existence: these VIRTUAL PARTICLES are not directly observable, but have well verified effects.

In the false vacuum, the energy is in the form of an inflaton: a field of force (somewhat analogous to electric and magnetic fields) that has a fluctuating value: the fluctuations may be thermal (SC-29).

The inflaton usually resides in a high energy state, but a fluctuation in a small region can cause the inflaton to fall into a low energy state or true vacuum.

The inflaton exerts a NEGATIVE PRESSURE and therefore a REPULSIVE GRAVITY (Gr-281--283).

When the inflaton falls to the low energy state or true vacuum, the energy released from the inflaton manifests itself as a super expansion caused by the REPULSIVE GRAVITY (which is the inflation itself) of the small region of space, the quantum mechanical creation of all kinds of particles (quarks, leptons, photons, exotic particles and their antiparticles, except that photons are there own antiparticles) during the inflation, and super-heating as the inflation comes to an end.

Unlike the cosmological-constant dark energy, the energy of the inflaton varies in time and in fact exhausts itself during inflation.

A cartoon of the inflation epoch.

The inflation creates the conditions of the early big bang epoch at some small time (e.g., 10**-32 s [FK-661]) after when the Big-Bang singularity would have happened in a pure Friedmann-Lemaitre-Lambda models.

The numbers associated with inflation are quite uncertain because no one knows the exact properties of of the false vacuum or of the inflaton.

High energy particle physicists can only make crude estimates based on what they think the appropriate physics should be like.

A cartoon of the growth of an inflation region.

You can see our universe domain may have started out as a microscopic speck---albeit one with the all the energy needed to make the huge space we live in.

What does the inflated region (i.e., the universe domain) look like from the outside?

It may look like a small black hole, but because of the internal expansion, one without a singularity at the center: i.e., a black hole with a difference (SC-23).

Outside it may be a Hamlet's ``nut shell.''

If this is literally true, stuff from outside could fall into our universe domain, but can't get out---but where it would arrive and how would it appear and what would it be?

Question: Was the speck of background universe that became our universe domain the only inflated domain of the background universe?
1. Certainly yes.
2. Absolutely no.
3. It seems very reasonable to believe that it was not unique. There may be many, maybe infinitely many other somewhat similar universe domains.












There is no right answer.

But answer 3 is what many people think is plausible.

The general picture of eternal inflation is that the background universe is infinite and eternal and sprouts infinitely many universe domains. The background universe is the multiverse.

However, the low-energy physics in other domains could be quite different from ours. The setting of the low-energy physics may be random.

The high-energy physics is assumed to be general. Also conservation of energy and 2nd law of thermodynamics are taken to be general. Without these concepts, we would have little guidance for understanding the multiverse.

Most other universe domains may in fact be rather dull: no stars or galaxies may form or atoms may be unable to form or the domain may collapse to the quantum gravity equivalent of a black hole singularity (SC-23).

Some of the coincidences of our universe domain may be explicable by invoking the anthropic principle. But anthropic principle arguments are often hard to make convincing although they often seem plausible.

Philosophically, eternal inflation is satisfying to many people: infinite and eternal and on a super-large scale homogeneous, isotropic, and unchanging with time.

Eternal inflation, in fact, resembles the Steady State Universe in being infinite and eternal and on a super-large scale homogeneous, isotropic, and unchanging with time.

Fred Hoyle (1915--2000) should have approved of eternal inflation. But I can't find any evidence that he did.

But, of course, eternal inflation is only one of many inflation theories: they may none of them be right.

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How well supported is the idea of inflation?

1. It provides possible solutions for the three problems discussed above.

   It remarkably predicted Omega equal to 1 to within 1 in 10**5 (CL-155) long before observations gave Omega=1.02+/-0.02 (FK-653).

2. Physicists find it plausible in terms of modern theories of particle physics.

   In fact, the belief is that particle physics and cosmology are essential to each other, not just mutually illuminating: you have to understand both to understand the one.

3. For what it is worth, some versions of inflation like eternal inflation are philosophically satisfying to many.

But is there more evidence for inflation?

Yes.

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Cosmic microwave background radiation (CMB) power spectrum from WMAP (2003).

These plots are rather difficult to interpret simply.

But rather vaguely, the top plot shows of frequency of hot and cold spots of various angular sizes on the sky (FK-652--653). Large spots are on the left; small spots on the right.

The data points come from the WMAP satellite and other detectors.

The curve is fit to the data???---but with how many free parameters---of what is called a scale-invariant power spectrum which is a prediction of most inflation models irregardless of the details of the inflation mechanism (CL-263,265,274--275; Gr-309).

The fact that inflation predicted the observations is an astonishing triumph of the inflation idea.

It does NOT prove inflation, but it certainly strongly supports it.

Credit/Permission: NASA/WMAP Science Team / Public domain.

Download site: NASA/WMAP Science Team: Images: Other Images, but this particular image no longer seems be posted.

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The upshot is that the idea of inflation has some strength and has increased in strength with time: it hasn't simply gone away as some new concepts do.

But we still don't know the true physics of inflation. All particle physicists can give us is ideas that are plausible to them.

And there is a rival theory of the larger universe: the ekpyrotic universe which does as well as inflation according to its proponents (FK-676). It is based on string theory.

We will not discuss the ekpyrotic universe further here---the instructor hopes it will just go away. Maybe string theory will go away too.

However, inflation and the ekpyrotic universe do make different predictions about the redshifts of distant galaxies and the polarization of the CMB.

So which idea is favored may emerge soon.

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Conclusion

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Modern cosmology has seen many changes in observations and theory since beginning with Einstein and the Einstein universe in 1917 (No-520; Bo-97).

One can cite a representative sample of the major innovations:

1. 1917: The Einstein universe (No-520).
2. 1920s: The Friedmann-Lemaitre models (No-524--525).
3. 1929: The observational discovery of the expansion of the universe and Hubble's law (No-523).
4. 1930s: Lemaitre's primeval atom (No-530) and the first observational evidenced for dark matter.
5. 1940s: Big Bang cosmology (No-531ff,559ff).
6. 1952: The major revision of the Hubble constant (No-528).
7. 1965: The CMB observationally discovered (No-560ff).
8. 1970s: inflation cosmology (FK-661; Ov-240,242,245).
9. 1980s: Dark matter universally accepted as the leading theory to explain large scale motions. MOND remains challenger theory.
10. 1990s: The observational discovery of fluctuations in the CMB (FK-640,644).
11. 1998: The acceleration of the expansion of the universe (FK-649).
12. 2000s: Detailed CMB maps and the concordance model (FK-653).

Are more changes are coming?

Well very probably yes, although Big Bang cosmology as far as it goes seems robust.

Here are some questions:

1. Will the formation of large-scale structure continue to firm up? Probably. Seems to be doing better all the time.
2. What is the ordinary dark matter? The theory that it is mainly intergalactic medium seems to be firming up.
3. What is the dark matter? We have some hope---but by no certainty---that it might be discovered within a few years or decades.
4. What is the dark energy? We are still pretty clueless. There is more accessible observational evidence to obtain.
5. Will inflation continue to provide a useful framework in which to analyze the larger universe or multiverse?
6. Will MOND become important or will it go away. It seems to be losing the battle to dark matter, but it may stage a comeback.
7. Will particle physics and cosmology solve all their joint problems giving us the theory of everything (TOE) and the true theory of cosmology? Who knows.

Some of these questions might see rapid development; others could take a long time.

In any case, as people are fond of saying, we are in the golden age of cosmology (since circa 1992).