Sections
But, of course, it is NOT the science of everything.
We covered the large-scale structure in IAL: The Large-Scale Structure of the Universe and can only recapitulate that coverage a bit here in IAL 30: Cosmology.
As an illustration of the large-scale structurelarge-scale structure, see the figure below (local link / general link: large_scale_structure_z_0x035.html) of the local large-scale structure to cosmological physical distance ∼ 150 Mpc (cosmological redshift z ≅ 0.035) and cosmological physical distance ∼ 300 Mpc (cosmological redshift z ≅ 0.07).
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, electrons, neutrinos, quarks, photons, and dark matter particles (if they exist).
The understanding of the smaller things is only needed insofar as it affects the big things.
In fact, the primary physics essential for cosmology is general relativity.
General relativity is exemplified by curving space, gravitational lensing, and black holes. These effects/objects are illustrated in the two figures below (local link / general link: spacetime_curvature_earth.html; local link / general link: black_hole_gravitational_lensing.html).
It is our best theory of gravity and motion under gravity so far.
And it is gravity that determines the motion of the universe as a whole and the evolution of the large-scale structure to first order.
Newtonian gravity was shown to be inadequate for cosmology as we will discuss below in the section The Early History of Cosmology. So, indeed, the more general theory, general relativity, is needed.
See Isaac Newton (1643--1727) in the figure below (local link / general link: newton_principia.html).
Whatever, quantum gravity may be, it will probably have implications for cosmology beyond Λ-CDM model (which we describe below in section The Λ-CDM Model) and which mostly adequately accounts for the observable universe so far. But some revision or replacement in the near future is likely.
In addition to general relativity, cosmology also requires classical physics (including thermodynamics), statistical mechanics, nuclear physics, quantum mechanics, and quantum field theory (which is relativistic quantum mechanics). For the most prominent branches of physics, see the figure below (local link / general link: physics_branches.html).
There are many things which are definitely excluded from cosmology: e.g., planets, biology, humans, psychology, the Oedipus complex (see the figure below: local link / general link: sigmund_freud.html), etc.
Big Bang cosmology (AKA the Big Bang theory) is the paradigm (i.e., overall grand theory) of cosmology and has been so since the 1960s. It is so well established that it would be astonishing if it were just plain WRONG.
So Big Bang cosmology is NOT speculative science anymore: it is probably essentially right as far as it goes.
The particular quantitative version of Big Bang cosmology that now holds sway is the Λ-CDM model which mostly adequately accounts quantitatively for the observable universe so far.
However, NEITHER Big Bang cosmology NOR the Λ-CDM model in themselves tell us everything we would like to know.
We take up this subject in detail in section Limitations and Tensions of our Current Cosmological Theories.
Issues outside of Big Bang cosmology are dealt with in broader theories which could better be called paradigms (i.e., overall grand theories). Those paradigms are more speculative and may well be just WRONG.
Currently, only two beyond-the-Big-Bang paradigms have much of a vogue: inflation (very much the frontrunner) and the cyclic universe in various versions (e.g., the ekpyrotic universe) (very much the hindmost).
We will discuss inflation and, briefly, the cyclic universe below in the section Inflation and Inflation Cosmology.
But we will give a brief introduction to inflation here.
Inflation is actually paradigm with many precisely specified versions: i.e., theories of inflation.
Basic inflation sets the initial conditions for the Big Bang in a rather satisfying manner.
But we do NOT know which of the precisely specified theories of inflation is correct if any NOR even which one is most adequate.
In the opinion of many, inflation is a useful paradigm for furthering research, but NOT yet a well established paradigm.
Beyond basic inflation are more elaborated, speculative versions of inflation (NOT essential to the inflation paradigm) which try to explain the universe as a whole, observable and unobservable.
A prominent one of the speculative versions is called eternal inflation.
Eternal inflation and some other speculative theories invoke the paradigm of the multiverse.
The multiverse is a paradigm for the universe as whole, observable and unobservable.
Note multiverse is just a special name for the universe as whole.
The multiverse is is highly speculative, but there is some evidence for it.
Eternal inflation is one version of the multiverse as well as being one version of inflation.
The eternal inflation version of the multiverse (as most people think of it, it seems) consists of a background universe consisting of some kind of fields understandable in quantum field theory and an infinity of pocket universes.
What are pocket universes?
Large regions in which particular initial conditions or even some physical laws are realized out of some infinity or quasi-infinity of possibilities allowed by quantum field theory, high energy physics, general relativity, quantum gravity, and thermodynamics.
The observable universe is embedded in "our pocket universe". We CANNOT see any trace of its edges wherever they are so far. We may be deep in the interior.
What separates the pocket universes?
In eternal inflation, there may be large, smoothly-varying transition regions of high-energy vacuum (called false vacuum which we discuss briefly below in the section Inflation and Inflation Cosmology).
But perhaps there are sharp boundaries.
Note that the eternal inflation multiverse is still governed by general relativity and this implies it CANNOT be static---it may be in overall expansion or constraction, but probably NOT uniformly: there may be some complex mixture expansion and constractions.
See the cartoon of the eternal inflation multiverse in the figure below (local link / general link: inflation_eternal.html).
Note we have to impose some restrictions on the possibilities for physical laws or else we have no guidance for explicating the multiverse and admit we know nothing---perhaps we do know nothing.
The concepts of multiverse and pocket universe are very speculative. They may NOT exist. But they are persuasive to some.
And they have become necessary in discussing modern cosmology.
The consensus is that we usually use the term universe for the structure that includes and resembles the observable universe.
So we need other terms that for the universe of everything physical.
The terms/concepts multiverse and pocket universe fill that need.
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.
See angel of melancholia reflecting on the meaning, purpose, and nature of the universe in the figure below (local link / general link: melancholia.html).
Modern physical cosmology of course, concerns itself with NATURE OF and leaves aside MEANING AND PURPOSE.
But MEANING AND PURPOSE probably hover somewhere just beyond the expressed concerns of many modern scientific cosmologists and are probably of interest to everyone interested in cosmology.
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 a let-down.
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. But one can ponder: see the figure below (local link / general link: the_thinker.html).
One can go the other way and try to derive or constrain cosmology from philosophical ideas.
Using philosophical ideas as a source of interesting cosmological hypotheses in research via scientific method is valid as long as the hypotheses are NOT taken as dogma, but as things to be tested empirically.
For an example of a reluctant cosmologist, consider cosmologist Georges Lemaitre (1894--1966) who was a Roman Catholic priest.
Lemaitre resisted identification of his primeval atom theory with the creation of Genesis. The former was speculative science; the latter, faith.
The primeval atom is the theoretical ancestor of Big Bang cosmology (see No-525,530; Jean-Pierre Luminet, The Rise of Big Bang Models (4) : Lemaitre, 2015).
Images of Lemaitre are given in the figure below (local link / general link: georges_lemaitre.html).
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.
See a couple of the old bulls in the figure below (local link / general link: aristotle_plato.html).
Who's to say when the next great advance in understanding in philosophy will come and clarify things for us.
As the figure below (local link / general link: pan.html) suggests perhaps one is forced to admit "Those cosmologists, they don't know nothing."
See the discussion in the figure below (local link / general link: leonardo_da_vinci_deluge_creation.html).
But is this true? Certainly, modern physical cosmology thinks so---in time and/or outside of time.
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 investigation, 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 (see Wikipedia: Democritus: Anthropology, biology, and cosmology). See the two figures below (local link / general link: democritus.html; local link / general link: cosmology_atomist.html) and the subsection Early Cosmology Videos at the end of this section.
The figure below (local link / general link: gemini_north_swirl.html) showing a long-exposure image makes Democritus' thinking plausible.
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.
In western Eurasia, the cosmological theory that became dominant in Classical Antiquity and then in the Islamic Golden Age (c.8th--c.14th centuries) (see figure below) ...
Caption: At the Alhambra in Granada, Spain: "A room of the palace and a view of the Court of the Lions."
Credit/Permission: Adolf Seel (1829--1907),
1892
(uploaded to Wikipedia
by Andreas Praefcke (AKA User:AndreasPraefcke),
2006) /
Public domain.
Image link: Wikipedia:
File:Adolf_Seel_Innenhof_der_Alhambra.jpg.
... and Medieval Europe (see the figure below: local link / general link: joan_of_arc.html) ...
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.
See a cartoon of Aristotelian cosmology in the figure below (local link / general link: aristotle_cosmos.html).
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.
Answer 2 is right.
You are beginning to get the idea. Some ancient Greek has thought of everything first.
For Aristarchos of Samos (c.310--c.230 BCE), see the figure below (local link / general link: aristarchos.html).
But if the stars were very remote why should they be pasted on a big sphere (the celestial sphere of the stars)?
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 (1546--1595) in 1576 (No-296). See the figure below (local link / general link: copernican_cosmos_digges.html).
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) (see the figure below: local link / general link: newton_principia.html) 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.
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 extent 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 did NOT like to publish half-baked ideas, and this is probably why he NEVER published his cosmological ideas. He liked ALL-BAKED publications. Also, he does NOT seem to have spend much time thinking about the universe as a whole.
Attempts in the 19th century to create a Newtonian theory of the whole universe also 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 extra hypotheses about physical laws (Bo-75,78).
But one could have an infinite empty-space universe, except for 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 did NOT catch on for reasons that are NOT clear. It seems perfectly sensible.
People, starting with Newton, seem fixated with the idea that the universe should be STATIC overall. This may be because Newton believed his theory of absolute space (i.e., a fundamental inertial frame in which the stars were at rest, at least on average) was essential.
Of course, Wright thought it possible that there were other galaxies (see Wikipedia: Thomas Wright: Life and works)---the first person known to have done so.
What if they existed? What would keep groupings of galaxies from all collapsing into ever larger clumps under self-gravity if they had started out forming as static distribution for some reason?
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.
See the Early cosmology videos below:
Form groups of 2 or 3---NOT more---and tackle Homework 4 problems 8--13 on ancient Greek astronomy.
Discuss each problem and come to a group answer.
Let's work for 5 or so minutes.
The winners get chocolates.
See Solutions 4.
After the Copernican revolution of the 16th and 17th centuries, the vague ideas of the universe as quasi-infinite with a quasi-infinity of stars gained ground and Newton believed them as we mentioned above in subsection Isaac Newton (1643--1727) and the Universe.
From 17th century to the early 20th century, the vague ideas astronomers had on the universe evolved a bit. It seems that they thought either there was a finity of stars in the Milky Way with nothing beyond OR there was a quasi-infinity of stars organized into galaxies which extended to quasi-infinity.
Without polls from the past, it's hard to know what were the actual opinions of astronomers back then.
The definitive proof of the existence of other galaxies in 1924 (see Wikipedia: Edwin Hubble: Universe goes beyond the Milky Way galaxy; No-510) clarified one issue.
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.
Heat energy is steadily being lost to stars as energy flows out of them in the form of electromagnetic radiation (EMR) and NOT being returned.
Even before the development of thermodynamics in the 19th century, people were aware in sense of the problem of universe NOT being in thermodynamic equilibrium in a sense via Olbers's paradox: see figure below (local link / general link: olbers_paradox.html).
But the heat energy flow from stars clearly proved space in some sense had to be much colder than stars even to people well before 1900.
To us, it seems natural to think it could be evolving in other ways, but somehow this idea was resisted before circa 1920.
Actually there was evidence before 1920s for large-scale motions of the universe.
See the figure below (local link / general link: vesto_slipher.html) on the work of Vesto Slipher (1875--1969).
The cosmological redshift is explicated (along with some discussion of the Doppler effect) in the figure below (local link / general link: cosmological_redshift.html).
Answer 1 is right.
In 1924, Hubble had shown that the Andromeda spiral nebula (M31) was another galaxy and by implication all other spiral nebulae were too (see Wikipedia: Edwin Hubble: Universe goes beyond the Milky Way galaxy; 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 1924 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.
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 distances to 46 galaxies beyond the Milky Way including 4 in the Virgo Cluster (a nearby large galaxy cluster) (Wikipedia: Edwin Hubble: Redshift increases with distance; Hubble 1929; No-510, but some errors). But only 24 of these distances were for independent and could be used in his analysis???.
Note that Hubble could only get Cepheid distances to the Andromeda Galaxy (M31) and the Triangulum Galaxy (AKA M33) ??? (No-510). That is about as far as he could observe Cepheids. For greater galaxy distances, he had to use less-reliable distance indicators from his early version of the cosmic distance ladder. Those less-reliable distance indicators had large systematic errors and random errors. So his distances were NOT too good---but they were good enough for his most famous discovery.
However, as described above, the 1st order Doppler shift formula, agrees to the 1st order with the cosmological redshift formula. Thus, whatever Hubble's exact thinking, he was still able to find the correct law describing the expansion of the universe.
Hubble extracted Hubble's law from a Hubble diagram.
For Hubble's law and a modern Hubble diagram for the very nearby local universe, see the figure below (local link / general link: hubble_diagram.html). A more detailed caption appears in the next subsection (i.e., subsection The Hubble Diagram).
Actually, it is the relative rate of expansion of the universe (i.e., the ate of expansion of the universe per unit cosmological physical distance) This is clear from the formula above with the interpretation of r as cosmological physical distance: i.e., the distance measured at one instant in cosmic time (which we discussed in IAL 26: The Discovery of Galaxies and which we will discuss further below).
Hubble's original favored value for H_0 (which he called K) was 500 (km/s)/Mpc (Hubble 1929, 3rd to last paragraph; Bo-39; Tamann 2005; Wikipedia: Timeline of Hubble constant values).
Hubble had large systematic errors in his distance values, and so his value for H_0 was rather badly wrong.
Circa 2021, the value of the Hubble constant has NOT been absolutely agreed. Two possibilities that do NOT agree within error are ∼ 68 (km/s)/Mpc and ∼ 73 (km/s)/Mpc (see Wikipedia: Timeline of Hubble constant values) .
For this lecture, we will usually write
H=70*h_70 (km/s)/Mpc, where h_70=H/(70 (km/s)/Mpc) is 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. The fiducial value must be correct to within a few percent.
Hubble's law shows that there is a general expansion of the universe and that the relative rate of expansion. Hubble constant.
So Hubble had observationally discovered the expansion of the universe and that it obeyed Hubble's law.
However, there was some debate how about how much credit Hubble should get and how much others should get. We take up this fine point in the history of astronomy in subsection Who Discovered the Expansion of the Universe and Hubble's Law? in section Friedmann-Equation (FE) Models below.
Hubble extracted Hubble's law from what we now call a Hubble diagram as aforesaid in subsection Hubble and the Expansion of the Universe.
See the example Hubble diagrams in the figure below (local link / general link: hubble_diagram.html).
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.
The first 3 answers are all partially right. Together they constitute what we believe to be the right answer.
They are just what one ordinarily means by distance.
But cosmological physical distances are NOT direct observables, except asymptotically as cosmological redshift z becomes small.
We discuss cosmological models below: see section Einstein, General Relativity, and the Einstein Universe and subsequent sections.
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 about the z ≤ 0.5 local universe. They are dependent on the cosmological model adopted, and so have that model's uncertainty.
We CANNOT observe galaxies and other remote objects (e.g., quasars, supernovae, and gamma ray bursts) at the current cosmic time, but only as they were in the past.
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 adopted.
Well either answer could be right logically speaking.
But answer 2 is so overwhelmingly more acceptable that we must accept it as right.
There may be a center of expansion in some sense if we live in a pocket universe, but we have NO where that is if it exists.
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.
But is there a center of expansion of our pocket universe if we are in one and edge too it. There are speculative theories as discussed above in subsection Beyond Big Bang Cosmology, but we do NOT know.
The figure below (local link / general link: expanding_universe.html) shows how to understand the expanding universe.
Is there a center of expansion?
In Friedmann-equation (FE) models (see section Friedmann-Equation (FE) 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 FE 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:
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.
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.
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.
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.
Form groups of 2 or 3---NOT more---and tackle Homework 30 problems 2--5 on cosmology and Hubble's law.
Discuss each problem and come to a group answer.
Let's work for 5 or so minutes.
The winners get chocolates.
See Solutions 30.
Hence, Einstein went on to develop general relativity with the complete theory presented in 1915.
In this section, we reference our presentation of general relativity in subsection General Relativity and then go on to see how Einstein applied it in cosmology.
Einstein (see figure below: local link / general link: einstein_master_1921.html) posited general relativity as a universal physical law which means it should apply everywhere in the universe.
But that means general relativity should apply to the largest scale structure of universe assuming that gravity determines the largest scale structure of the bulk universe---which we believe to be true.
In other words, if general relativity was truly a universal physical law, it must be able to give self-consistent cosmological model.
Showing that it did so was a necessary verification of general relativity and Einstein did, in fact, pursue that verification.
Note Einstein's immediate concern was that such self-consistent cosmological model was possible, NOT that it was the actual true self-consistent cosmological model of the universe. But Einstein did eventually come to hope that his cosmological model, which we call the Einstein universe, would be the right one. We know this because it took him a long time to 1931 abandon it. He only did so after accepting the expansion of the universe (two years after Edwin Hubble (1889--1953) had shown it definitively in 1929) and some years after the Einstein universe had been shown to be unstable: i.e., it would necessarily evolve into a cosmological model with expanding and/or contracting regions (see Cormac O'Raifeartaigh et al., Einstein's 1917 Static Model of the Universe: A Centennial Review, 2017, p. 40--41).
The Einstein universe, was presented in 1917 (Bo-97; No-520; Cormac O'Raifeartaigh et al., Einstein's 1917 Static Model of the Universe: A Centennial Review, 2017; Cormac O'Raifeartaigh, Historical and Philosophical Aspects of the Einstein World, 2019).
A finite system of galaxies held from collapse by rotation in an infinite, otherwise empty outer space seems a possible pure Newtonian physics cosmological model to yours truly. However, all kinds of questions would arise then how such a cosmological model would evolve in time.
In order to apply general relativiey (GR) to the universe, Einstein made 3, major simplifying ASSUMPTIONS, the first 2 of which are still usually used today at least for theories of our universe (or our pocket universe) when NOT including large-scale structure of the universe.
We explicate the made 3, major simplifying ASSUMPTIONS in the subsubsections below.
The cosmological principle is a glorified expression for the assumption that the universe looked at averaged over sufficiently large scales is homogeneous (i.e., the same everywhere at one time) and isotropic (i.e, the same in all directions).
The cosmological principle is explicated in the figure (local link / general link: observable_universe_cosmological_principle.html).
So for Einstein, the universe was one full of stars, NOT galaxies and the cosmological principle for him meant that the stars were homogenously and isotropically spread throughout space
By the by, Einstein's knowledge of astronomy was NOT extensive in 1917 though in later years he became much more knowledgeable.
The term cosmological principle was NOT used by Einstein at least NOT in 1917. It was coined in 1935 by E.A. Milne (1896--1950): see the figure below local link / general link: e_a_milne.html.
This assumption is that the mass-energy of the universe can be approximated as a homogeneous, isotropic, perfect fluid which in the older literature was sometimes called the substratum (Bo-65,75--76).
A perfect fluid has NO heat conduction, NO viscosity, and NO shear stress. It can have pressure. In cosmological models baryonic matter is assumed to have zero pressure---which is a good approximation in cosmology though NOT in other fields astrophysics (see Li-39). The cosmic background radiation (CBR) has significant pressure only at very early times in Big Bang cosmology: i.e., at cosmic time < ∼ 50,000 years after the Big Bang (see radiation era). Dark energy formally has NEGATIVE PRESSURE, but since it does NOT pull on anything, in fact, this NEGATIVE PRESSURE is sort of mythical. We discuss dark energy below in subsection The Introduction of the Cosmological Constant.
Einstein assumed zero pressure which, in fact, all cosmological models did (except near the very near Big Bang era) before circa 1998.
By using the perfect fluid assumption Einstein universe and, in fact, most cosmological models for the observable universe do NOT deal directly with stars, galaxies, and the large-scale structure of the universe. So now for a question on assumptions in theorizing.
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 CANNOT 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 do NOT know how to deal with anyway: i.e., crawl before walking.
So answer 4 is always a good idea. It is a roundabout way of expressing Occam's razor.
Einstein assumed the universe was static which in fact is a WRONG assumption since there is an expansion of the universe, but this was NOT known until the 1920s either observationally or theoretically. There may have been a few astronomers thinking of it for hypothetical other galaxies, but Einstein (who had a non-astronomy background) was probably NOT aware of that thinking.
Recall that for Einstein in 1917 the universe was one full of stars, NOT galaxies and the cosmological principle for him meant that the stars were homogenously and isotropically spread throughout space (see the subsubsection The Cosmological Principle Assumption above).
So by a static universe, Einstein was thinking of a static distribution of stars.
Why did he make this assumption?
Possible and certain reasons:
This is a certain reason.
Perhaps, they were still thinking of the stars as being at rest in Isaac Newton's (1643--1727) absolute space.
It's hard to know what was majority opinion in 1917 since there are NO opinion polls from 1917 on cosmology.
So it may be that Einstein was simply following what he believed to be the general belief that the universe was static.
This is a possible reason.
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.
If so, this was wrong as we now know. But we know this because we have the Friedmann equation which is derived from general relativity. Somehow Einstein missed deriving the Friedmann equation and derived the Einstein universe directly from general relativity in a klutzy way. It was a pioneering effort.
In later years, Einstein (or so yours truly recalls from some long ago reading) dismissed Mach's principle as perhaps wrong since it is NOT inherent in general relativity and was NOT required by cosmology as it had developed.???? The situation is the same today: Mach's principle may have some truth to it, but nothing demands it. In fact, there seems little interest in Mach's principle anymore.
In fact, Einstein found that he could NOT find a STATIC MODEL or ANY MODEL with GR as he had originally proposed it (No-520).
So he introduced the cosmological constant which we explicate in the insert below (local link / general link: lambda_cosmological_constant_dark_energy.html).
Einstein's STATIC MODEL is now called the Einstein universe. Geometrically, it is the 3-dimensional surface of a sphere in a 4-dimensional Euclidean space. Such a "sphere" is called a hypersphere. Thus, the Einstein universe is a finite, but unbounded, hyperspherical space (No-520; Bo-98).
Note, the 4-dimensional Euclidean space is given NO physical interpretation since general relativity does NOT imply it exists in any sense. There is just the curved "surface space".
One source (No-513) claims that the Einstein universe is a 3-dimensional surface of 4-dimensional cylinder. But this seems to be just a mistake. See Jones et al. 2003 for the correct description.
The Einstein universe is analogous to the surface of an ordinary sphere in the figure below (local link / general link: universe_geometry.html).
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 in one direction you should see the back of your head.
A "straight line" in curved space is geodesic---the stationary path (the shortest path in most considered examples) between any two points in the curved space.
The Einstein universe is actually in unstable equilibrium (Bo-118; No-527). Any perturbation will start it on a runaway expansion or contraction.
The cartoon in the figure below (local link / general link: stability_mechanical.html) illustrates stable and unstable equilibriums.
Exactly how the many local perturbations that exist in any real universe could have affected a real Einstein universe is hard to say. However, one idea of how a perturbed Einstein universe would behave is discussed below in subsection Avoiding the Singularity.
After 1929 and the observational discovery of expansion of the universe (No-523) and discussions with many researchers including Edwin Hubble (1889--1953) in 1930 (No-526), Einstein abandoned the Einstein universe and subsequently very probably said introducing the cosmological constant to obtain the Einstein universe was his "biggest blunder" (though only in private and perhaps NOT in those exact words: he may have been speaking in German) to George Gamow (1904-1968) and maybe others (see O'Raifeartaigh &Mitton 2019, p. 22--23).
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 for other cosmological fix-ups---"the last refuge of scoundrel cosmologists" (Michael Turner 2011)---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-equation Λ Models.
But though Einstein blundered, others did NOT: expansion of the universe was predicted from GR models before it was observationally discovered as we'll see below in the section Friedmann-Equation (FE) Models.
See Einstein videos below (local link / general link: einstein_videos.html).
Form groups of 2 or 3---NOT more---and tackle Homework 30 problems 2--8 on cosmology, Hubble's law, and the Einstein universe.
Discuss each problem and come to a group answer.
Let's work for 5 or so minutes.
The winners get chocolates.
See Solutions 30.
FE models begin from a singularity of infinite density---with a couple of exceptions to be mentioned in subsection Avoiding the Singularity below.
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.
How big is the singularity in its theoretical context of taking the FE models as exactly true? Well if the universe is infinite, it's infinite or indeterminate. And if the universe if finite, it's a point.
But modern cosmologists do NOT think the singularity actually existed. Taking the FE models as exactly true at the singularity is pushing them beyond their validity since you reach infinite density. Infinities in physics usually mean that you have pushed a theory beyond its realm of validity. That seems likely to be the case for FE models at the singularity.
Nevertheless, the singularity is the time zero of the FE models: those that a have singularity that is. It is though of as being approached, but NOT reached.
And the time of the singularity is still used as fiducial time zero of cosmic time with the understanding that it probably never happened. It is just beyond the limit of the time where we can extrapolate established physics which is the quark era (10**(-12) -- 10**(-6) s.
What happens instead of the singularity? Quantum gravity and perhaps other effects must supercede general relativity as infinite density is approached. We discuss the main ideas of what happened in section Inflation and Inflation Cosmology.
The FE models that have NO singularity and infinite age if their mass-energy is constant in time as they expand.
Such models are, in fact, versions of the de Sitter universe (see section The de Sitter Universe above).
Another way to avoid the singularity is to start a model from an Einstein universe. Recall the Einstein universe is unstable, and so the right kind of global perturbation will start it growing and it will evolve asymptotically to a de Sitter universe. Local contracting perturbations were thought of as perhaps being the origin of galaxies (Bo-120). This cosmological model is called Lemaitre-Eddington universe (see, e.g., Bo-84,85,117--121,159,175,180; No-527). It had a vogue circa 1925--1935 when it was favored by Arthur Eddington (1882--1944), but NOT by Georges Lemaitre (1894--1966) at least after circa 1931 (see, e.g., Bo-84,85,117--121,159,175,180; No-527).
A version of the de Sitter universe is the famous/notorious Steady State Universe which is elucidated in the figure below (local link / general link: fred_hoyle.html).
Hereafter, for simplicity, we will mean finite-age FE model with a singularity when we say FE model.
In modern Big Bang cosmology, the term Big Bang is generally taken to mean the era from time zero (i.e., Big Bang singularity) to about 20 minutes.
During this time, the light elements of the universe (hydrogen, deuterium, helium, and some lithium) are believed to have been synthesized in Big Bang nucleosynthesis era (cosmic time ∼ 10--1200 s ≅ 0.17--20 m).
We should emphasize that the Big Bang is NOT a pressure explosion where the kinetic energy comes from heat energy (CL-36) and pushes the mass-energy of the observable universe apart.
The space geometry of FE models is determined by the density parameter which has the symbol the capital Greek letter Ω and which is often just referred to as Omega. See the figure below (local link / general link: greek_letter_omega.html).
What the Friedmann equation (FE) actually gives is the cosmic scale factor a(t), where t is cosmic time.
The cosmic scale factor determines the scaling up of the expanding universe according to the formula
Note:
But also recall as we look farther out in space, we look further back in cosmic time, and so the present physical distances are NOT direct observables, except asymptotically as we approach r_0 = 0 since the time since light started out toward us goes to zero as r_0 → 0.
The scaling up is illustrated in the animation in the figure below local link / general link: expanding_universe.html).
The figure below (local link / general link: cosmic_scale_factor_lambda_zero.html) 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 FE Λ=0 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 pocket universe) 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 Λ-CDM Model.
In the Ω = 1 version, the slope of a(t) goes to zero asymptotically as cosmic time goes to infinity---so the universe comes to rest as cosmic time t → ∞ when a(t) = ∞.
If Ω > 1, then the universe (or pocket universe) will eventually recollapse and there will be a Big Crunch. See the cartoon animation of the Big Crunch in the figure below (local link / general link: big_crunch.html).
Since the Big Crunch is itself a singularity, we do NOT really know what happens then or later.
The cyclic universe as originally suggested has NOT lasted. There seems no way without ad hoc hypotheses to predict what happens as the universe passes through a Big Crunch.
But newer kinds of cyclic universe are thought to be viable: e.g., the ekpyrotic universe which we briefly discuss in the section Inflation and Inflation Cosmology.
A KEY POINT is that the FE Λ=0 models predict either an expansion or a contraction of the universe: i.e., a(t) is never constant, but always changing.
Hubble's law itself is a consequence of the FE models (with Λ=0 or not). This was shown explicitly by Georges Lemaitre (1894--1966) in 1927 as we discuss below in subsection Who Discovered the Expansion of the Universe and Hubble's Law?. See Georges Lemaitre (1894--1966) again in the figure below (local link / general link: georges_lemaitre.html).
Hubble's law can be determined empirically in a simple way from a Hubble diagram as did Hubble.
That Hubble's law can be determined empirically is proven using expanding universe models.
Luminosity distances (which we discuss below) and angular diameter distances (which we do NOT discuss) are direct observables.
It can be proven that these "distances" asymptotically approach the cosmological physical distance as cosmological redshift z goes to zero. This is illustrated in the cosmological distance measure graphs shown below (where "luminosity is luminosity distance and "angular diameter" is angular diameter distance).
The 1st order recession velocity, given by v_1st=zc, asymptotically approaches the exact recession velocity as cosmological redshift z goes to zero. This is illustrated in the cosmological distance measure graphs shown below since the "naive Hubble" divided by H is the 1st order recession velocity and the cosmological physical distance divided by H is the exact recession velocity.
Since the direct observable "distances" and the 1st order recession velocity approach, respectively, the cosmological physical distance and the exact recession velocity asymptotically as cosmological redshift z goes to zero, they must asymptotically satisfy Hubble's law (which holds exactly for cosmological physical distance and the exact recession velocity) as cosmological redshift z goes to zero.
Thus, as long as one observes cosmological objects at sufficiently small cosmological redshift z, one can find Hubble's law and the Hubble constant empirically from a Hubble diagram.
For the Λ-CDM model as seen in the cosmological distance measure graphs shown below, z must be less than about 0.5 to be sufficiently small.
The FE Λ=0 models in themselves do NOT tells us everything. In particular they do NOT tell us the values of the Hubble constant or 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-equation Λ Models.
But the fact that the FE Λ=0 models predicted the expansion of the universe before that was observationally well established and Hubble's law probably before it was known to the person making the prediction (i.e., Lemaitre's) is very impressive.
Answer 4 is right according to the best modern observations.
All the FE Λ=0 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-equation Λ Models.
But our discussion of the FE Λ=0 models has NOT been a waste of time as we will also see in the next section The Accelerating Universe and the Friedmann-equation Λ Models.
Now that we have discussed de Sitter universe and FE Λ=0 models, we are prepared to discuss this fine point of the history of astronomy. The figure below (local link / general link: georges_lemaitre_cartoon.html) gives the discussion.
Form groups of 2 or 3---NOT more---and tackle Homework 30 problems 6--11 on cosmology and the FE Λ=0 models.
Discuss each problem and come to a group answer.
Let's work for 5 or so minutes.
The winners get chocolates.
See Solutions 30.
How we got where we are now in modern cosmology with lots of omissions:
See Astronomer file willem_de_sitter.html for more detail on the de Sitter universe.
The most favored FE Λ=0 models was actually the Einstein-de Sitter universe (1932) which is NOT the Einstein universe (1917) NOR the de Sitter universe (1917). It is the simplest expanding universe FE model which is why Albert Einstein (1879--1955) and Willem de Sitter (1872--1934) proposed it (see Cormac O'Raifeartaigh, et al. 2015, arXiv:1503.08029). It has density parameter Ω=1 (and so has Euclidean geometry (AKA flat space geometry)) and cosmological constant zero (which is the same as NOT requiring the hypothesis of the cosmological constant). In proposing the Einstein-de Sitter universe (1932) in 1932, Albert Einstein (1879--1955) and Willem de Sitter (1872--1934) may have been trying to recapture the high ground from young upstart cosmologists: e.g., E.A. Milne (1896--1950), Georges Lemaitre (1894--1966), and William McCrea (1904--1999) (see also Wikipedia: E.A. Milne: Research into cosmology and relativity).
However, the Λ-CDM model was actually already being considered as a possible cosmological model by circa 1995 based some evidence and other considerations even before the discovery of the acceleration of the universe (see Douglas Scot, 2018, arXiv:1804.01318 "The Standard Model of Cosmology: A Skeptic's Guide", p. 10).
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 cosmological physical distances (except in a static universe or approximately for very small cosmological physical distances), but they are DIRECT OBSERVABLES.
We assume:
L F= -------- 4*π*r**2 where F is flux, L luminosity, and r distance. This formula implies r = sqrt[ L/(4*π*F) ] .
We can apply this distance formula to objects participating the universal expansion provided extinction is negligible or can be corrected for, and obtain "distances". But, of course, the "distances" obtained is NOT true distances (i.e., NOT a cosmological physical distance) since the observable universe evolves with cosmic time as the light propagates to us and may space may have an overall curvature.
So the formula distance r is a funny distance which because of the formula used to obtain it is naturally called luminosity distance.
Despite being funny, luminosity distances can be used, nonetheless, to determine cosmological parameters in a way we will NOT go into.
Luminosity distance is a DIRECT OBSERVABLE that cosmological models can be fitted to.
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 representative Hubble diagram is shown in the figure below (local link / general link: hubble_diagram_4.html).
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 FE Λ=0 models as aforementioned.
When the acceleration was first announced, people were somewhat skeptical.
The data had a lot of random errors---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:
The missing mass-energy can be interpreted as some kind of dark energy that is powering the acceleration.
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 shown in the figure below (local link / general link: adam_riess.html).
How does one accommodate the acceleration theoretically?
Well the possibilities are quasi-endless.
But the simplest way is to fetch Einstein's cosmological constant Λ back from the storeroom of discarded theories and put it back in the Einstein field equations and the Friedmann equation, but now tune it to give the measured acceleration instead of a static Einstein universe.
One can then derive what one can call the FE Λ models which are just the FE models with the cosmological constant Λ NOT zero. The value of Λ is NOT determined by the model and must be determined by observational or other means.
The cartoon plot in the figure below (local link / general link: accelerating_universe.html) shows how the cosmic scale factor a(t) evolves an appropriate FE Λ model.
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).
The name concordance model was once widely used, but has now fallen out of favor.
Note "Fit all all cosmological observations," EXCEPT for a few tensions (notably the Hubble tension since circa 2018) which we discuss below in section Limitations and Tensions of our Current Cosmological Theories.
So the Λ-CDM model may need some revision or even replacement as the standard model of cosmology (SMC).
For cartoon of cosmic cosmic history according to the Λ-CDM model and similar cosmological models, see the figure below (local link / general link: cosmos_history_2a.html).
The ingredient cosmological theories are:
Most obviously, the fitted FE Λ model gives the expansion of the universe with positive acceleration: i.e., the accelerating universe.
Big Bang cosmology gives the cosmic microwave background (CMB) and the cosmic composition as we will discuss below in the section Big Bang Cosmology and the Initial Conditions of the Observable Universe).
The Λ-CDM model is quantitative special case of Big Bang cosmology that may be right as far as it goes.
Cold dark matter is relatively slowly moving dark matter. We call it "cold" because it's moving at much less than the vacuum light speed c = 2.99792458*10**5 km/s ≅ 3*10**5 km/s.
If the dark matter were moving at relativistic velocities in the early observable universe, it would NOT have been able to clump on relatively small scales under its self-gravity to form gravitational wells which are essential to the large-scale structure that we observe (see Wikipedia: Cold dark matter: Structure formation).
Table: Cosmic Parameters below (local link / general link: cosmic_parameters.html) gives a representative set of values for the Λ-CDM model parameters.
We say "representative" because their is no single consensus set.
Various research groups using different analysis methods get slightly different sets and the parameter values will certainly change a bit more with future observations and analysis.
However, the differences among groups and with future work are likely to be less than 10 % or so.
The cosmic time of some important Λ-CDM model cosmic quantities is shown in the figure below (local link / general link: cosmic_scale_factor_lambda_cdm.html).
Some comments on the Λ-CDM model are:
If a model is wrong, then observations need to be interpreted in a different way.
Better observations could show inadequacy which, in fact, Hubble tension is suggesting right now (see section Limitations and Tensions of our Current Cosmological Theories below).
One generally starts with the simplest adequate theory in obedience to Occam's razor with the understanding that more elaborate theories may be needed as observations advance.
For example, a dynamical dark energy (i.e., a time-varying dark energy may be needed in a new standard model of cosmology (SMC).
The requirement for exotic dark matter is an inference as we will explain right now in brief.
Big Bang nucleosynthesis (which discuss below in the subsection Big Bang Cosmology) predicts Omega_baryonic matter ∼ 0.045, and the Planck spacecraft (2009--2013) observations plus other data give Omega_matter at 0.3147(74) (Planck 2018 results. I. Overview and the cosmological legacy of Planck 2018)
Big Bang nucleosynthesis is itself a very robust theory, and so we are forced to believe exotic dark matter is likely.
There are many ideas about what the new particle may be. One favorite idea is WIMPs (weakly interacting massive particles). But the possibilities are still wide open.
Anoher idea for dark matter is primordial black holes (PBHs) which we explicate in the figure below (local link / general link: black_hole_primordial.html).
If we ever discover what the dark matter is, it will have profound implications for cosmology and fundamental physics.
If MOND 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.
Baryonic dark matter is usually NOT included in dark matter, but sometimes it is. Context usually must decide what is meant.
We explicate baryonic dark matter just below in subsection Baryonic Dark Matter.
From Big Bang nucleosynthesis, Omega_ordinary_matter equal to about 0.045 (see Table: Cosmic Parameters above: local link / general link: cosmic_parameters.html).
But adding up all the stellar matter (i.e., baryonic matter which is NOT baryonic dark matter) gives only 0.004: see the figure below (local link / general link: pie_chart_cosmic_energy.html).
So baryonic dark matter is ∼ 10 times more abundant than stellar matter (i.e., baryonic matter which is NOT baryonic dark matter).
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/Permission:
User:Bryan Derksen,
2007 /
Public domain.
Image link: Wikipedia:
File:Relative_star_sizes.svg.
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 baryonic 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 baryonic dark matter ?
At present, the favored theory is that low-density nearly invisible primordial intergalactic medium (IGM) (hydrogen and helium gas) makes up most or maybe almost all of the baryonic 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 the gas falls into galaxy superclusters, galaxy clusters 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) along with somewhat 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 observed WHIM and yours truly thinks it is now established that WHIM is most of the baryonic 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????.
Form groups of 2 or 3---NOT more---and tackle Homework 30 problems 9--15 on cosmology, FE Λ=0 models, and the Λ-CDM model.
Discuss each problem and come to a group answer.
Let's work for 5 or so minutes.
The winners get chocolates.
See Solutions 30.
In other words, what is the Λ-CDM-model cosmic future.
A highly speculative sketch---which gets more speculative as it goes along---is as follows (HI-477, Wikipedia: Graphical timeline from Big Bang to Heat Death, Wikipedia: Future of the expanding universe):
Currently, we are at cosmic present = to the age of the observable universe = 13.797(23) Gyr (Planck 2018): i.e., at cosmic time = age of the observable universe = 13.797(23) Gyr (Planck 2018) ≅ 10**10 years counting from the Big Bang.
At cosmic time of order 10**14 years (∼ 10,000 times the current cosmic time), all star formation will have ended and all the long-lived M stars will have left the main sequence???. See the figure below (local link / general link: star_lifetimes.html).
The universe will consist of mainly of dark matter particles (probably and assuming dark matter is NOT primordial black holes (PBHs)), compact remnants (i.e., white dwarfs, neutron stars, and black holes), and uncollapsable H and He gas???.
Why does star formation turn off?
Well, a significant fraction of the baryonic matter (still mainly primordial hydrogen and helium gas) of the observable universe will have been turned into compact remnants, and will thus be unavailable for new star formation. This is probably the fate for baryonic matter trapped or still to become trapped in large gravitational wells.???
But the main reason??? is that the continued expansion of the universe (which recall is an accelerating expansion of the universe) will spread the intergalactic medium (IGM) (still mainly primordial hydrogen and helium gas plus dark matter) so much that it is uncollapsable into significant gravitational wells.
No more runaway gravitational collapses. No more star formation.
It is possible for quantum field theory reasons that protons radioactively decay (and this entails the radioactive decay of neutrons too) into electrons, positrons, neutrinos, and photons with a half-life of something in the range 10**31 to 10**36 years (see Wikipedia: Proton decay). Note there is NO experimental evidence for proton decay so far.
Assuming proton decay, at some cosmic time in excess of 10**31 years, the protons and neutrons will have all decayed. This will leave a dilute gas of electrons, positrons, neutrinos, and photons, and dark matter particles, and black holes.
Actually, dark matter particles may undergo spontaneous radioactive decay to Standard Model particles though there is NO accepted time scale (Wikipedia: Dark matter: Indirect detection).
For a dilute gas of photons, etc. in the heat death of the universe (which we discuss below in subsection The Heat Death of the Universe: Cosmic Time t >> 10**100 Years Years, see the figure below (local link / general link: heat_death_photons.html).
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, photons, and dark matter particles---if they have NOT undergone spontaneous radioactive decay to Standard Model particles (Wikipedia: Dark matter: Indirect detection).
Some hypothetical dark matter particles decay to baryonic matter with very long half-lives (see Wikipedia: Dark matter: Indirect detection). So maybe the dark matter particles will be gone too by of order 10**100 years ??? in the Λ-CDM-model cosmic future.
The expanding universe is now cold and dark and getting more so as the expansion continues---this is the heat death of the universe which was first discussed by William Thomson, Lord Kelvin (1824--1907) shown in the figure below (local link / general link: lord_kelvin.html).
See the image of photon gas in darkness in the figure above (local link / general link: heat_death_photons.html) in the figure below (local link / general link: lord_kelvin.html).
So the universe ends in ice metaphorically speaking---according to the Λ-CDM-model cosmic future.
The heat death of the universe as just described is the end of the story according to the Λ-CDM model---but there's NO reason to put much faith in it---it's a very speculative story.
It is, in fact, a wild extrapolation of the Λ-CDM model well beyond the observations it is fitted to. So it would NOT be surprising if the story got more and more wrong, the further in cosmic time it is extrapolated---but we may never know. See our story in the figure below (local link / general link: mayfly.html).
Recall, there are some tensions with the Λ-CDM model which we discuss in detail in section Limitations and Tensions of our Current Cosmological Theories. These could lead to a revision or replacement of the Λ-CDM model by a new standard model of cosmology (SMC).
With a new standard model of cosmology (SMC), we might have new wild extrapolation story for the far future.
So it is the explanation of the initial conditions of the observable universe (or of our pocket universe in the eternal inflation version of the multiverse paradigm).
In common modern usage, Big Bang means the early hot, dense phase of the observable universe.
The ancestor of Big Bang cosmology for the constituents of the observable universe was Georges Lemaitre's (1894--1966) primeval atom theory (1933)---but we won't discuss in detail that historically interesting, but long discarded, theory (No-530). See young Lemaitre (1894--1966) hanging out with the old guys in the figure below (local link / general link: georges_lemaitre.html).
In brief, the primeval atom theory posited a cold "Big Bang" in which a giant mass of neutrons (i.e., the primeval atom itself) filling a small positive curvature universe (a hyperspherical universe: finite, but unbounded). This small universe expanded according to a FE Λ≠0 model which we call the Lemaitre universe (1933). The primeval atom fragmented into smaller and smaller fragments of which the smallest are the hydrogen (H) helium (He). Larger fragments continue to exist and some are radioactive isotopes. These radioactive isotopes are inside stars and planets undergo radioactive decay: they power stars and provide radiogenic heat in planets.
The primeval atom theory (1933) was a brilliant theory and was viable circa in the 1930s. However, advances in nuclear physics and in the understanding of hydrogen burning in stars by the middle 1940s made it seem implausible and effectively ruled it out. Georges Lemaitre (1894--1966) himself continued to discuss the primeval atom theory (1933) in his later years while admitting he had become and old-fashioned cosmologist???.
In the 1940s (by which time nuclear physics was much more elucidated than in the 1930s), George Gamow (1904-1968) (see figure below local link / general link: george_gamow.html), 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.
But stars CANNOT account for the 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 far too much to have been produced in stars.
Recall the cosmic composition by mass is about the same as the solar composition: see below Table: Cosmic Composition (local link / general link: cosmic_composition_table.html).
The aforesaid light elements are accounted for by Big Bang nucleosynthesis. See Table: Cosmic Composition in the insert below (local link / general link: cosmic_composition_table.html).
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 CANNOT start the clock at the TIME ZERO of the Friedmann equation (FE) models since then there is infinite density (i.e., the Big Bang singularity) and general relativity must fail before that state is reached: we need a theory of quantum gravity to go the realm of super high densities and we do NOT have an established one (CL-122).
In fact, before about one Planck time (t_Planck ≅ 5*10**(-44) s) when density is very high our theories are very speculative. This period is called the Planck era.
The very earliest times before a second or so are in also in speculative realm (thought NOT as speculative as the Planck era) 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).
Caption: Quarks make up protons and neutrons.
Credit/Permission: ©
David Jeffery,
2004 / Own work.
Image link: Itself.
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.
It is thought in theories of particles that there is some asymmetry in properties between matter and antimatter that slightly favors matter (FK-668).
The usual assumption is that the early universe is isotropic and very homogeneous: i.e., among other things has nearly constant temperature, density, and composition at any given cosmic time.
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 continuous expansion causes the temperature and density to fall steadily. Recall the cooling is just due to adiabatic expansion.
The evolution of the cosmic temperature during cosmic time 10**(-10) s -- 10**16 s ≅ 0.3 Gyr which includes the early universe (10**(-12) s -- 380,000 y) is shown in the figure below (local link / general link: cosmic_temperature.html).
We will just give a simple presentation of the timeline of the early universe in a sequence of snapshots.
The captions are subject to revision from time to time, and so should NOT be taken as definitive.
The dark matter particles were omitted from the figures, but they should be assumed to be there too.
The snapshots:
At the electroweak era (t ∼ 10**(-36)s the strong nuclear force may have become distinct from the weak nuclear force and electromagnetic force which were still united as the electroweak force: i.e., the two acted in the same way. This era may have been just before inflation (see Wikipedia: Electroweak epoch.
The dark matter particles were omitted from this and following figures, but they should be assumed to be there too.
Credit/Permission: ©
David Jeffery,
2004 / Own work.
Image link: Itself.
Credit/Permission: ©
David Jeffery,
2004 / Own work.
Image link: Itself.
This was once thought to be about 3 minutes and hence the famous book The First Three Minutes, Steven Weinberg, 1977.
Credit/Permission: ©
David Jeffery,
2004 / Own work.
Image link: Itself.
Credit/Permission: ©
David Jeffery,
2004 / Own work.
Image link: Itself.
Circa 2023, early results from James Webb Space Telescope (JWST, 2021--2041?) suggest that galaxies may have formed as early as cosmic time t ≅ 0.35 Gyr (see J. O'Callaghan, 2022 Dec06, SciAm, "Astronomers Grapple with JWSTâ€™s Discovery of Early Galaxies"). If this result is confirmed, it may be another tension for the Λ-CDM model.
Credit/Permission: ©
David Jeffery,
2004 / Own work.
Image link: Itself.
The recombination era 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 era of about 3000 K (FK-670).
Before the recombination era, the photons interacted strongly with matter and thus matter and photons were held at the same temperature. At recombination itself this temperature was ∼ 3000 K as noted above.
After recombination era the primordial photons (i.e., cosmic background radiation) streamed off through space only slightly interacting with matter again.
The photons just after the recombination era had a blackbody spectrum at ∼ 3000 K and which according to Wien's law peaked in the near infrared (roughly 0.75--1.4 μm) at ∼ 1 μm. This cosmic photon gas for all eras is called the cosmic background radiation.
The primordial photons of the cosmic background radiation after the recombination era stream mostly freely through space. 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 cosmic background radiation would be ∼ 5 K (No-559).
Using Wien's law
2897.7685(51) μm*K λ_max = ------------------ ≅ 600 microns = 0.06 cm (T = 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.
The cosmic time of evolution of the temperature of the cosmic background radiation form well after the Big Bang nucleosynthesis (cosmic time ∼ 10--1200 s ≅ 0.17--20 m) and starting well into the radiation era (cosmic time ∼ 0--178.5 kyr) is shown in the figure below (local link / general link: cosmic_scale_factor_lambda_cdm.html).
The relic primordial photon gas (i.e., the cosmic background radiation) in the modern observable universe is called the cosmic microwave background radiation (CMB).
In 1965, Arno Penzias (1933--2024) and Robert Wilson (1936--) (see the figure below: local link / general link: arno_penzias.html) working with a Bell Labs radio telescope in Holmdel Township, New Jersey fortuitously discovered cosmic microwave background radiation (CMB, blackbody temperature T = 2.72548(57) K (Fixsen 2009)), but at only wavelength 7.3 cm in the microwave band (fiducial range 0.1--100 cm, 0.01--10 cm**(-1)). The CMB is a nearly uniform radiation field coming to us from all directions.
The first highly accurate CMB measurement over a broad wavelength range was reported from the COBE spacecraft circa 1990 (FK-640). The CMB sprectrum with data points from many observation devices is shown in the figure below (local link / general link: cmb_2.html).
The CMB has a large-scale variation (called the CMB dipole anisotropy) 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).
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 era.
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 local inertial frame in the direction the Hydra-Centaurus Supercluster (FK-640--641).
If the CMB dipole anisotropy is subtracted, there remain small-scale random fluctuations in CMB temperature of order 200 micro-Kelvins or in relative terms of 1 part in 10**5 (Wikipedia: Cosmic microwave background: Features). These fluctuations are formally called the CMB primary anisotropy.
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 (shown in the figure below local link / general link: cmb_wmap.html) 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).
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.
The comparison yields very favorable agreement, in fact.
But also it sets a limit on the density of baryonic matter (including the baryonic dark matter) in the observable universe. This limits only ∼ 1/6 of the dark matter needed to explain galaxies and galaxy clusters.
The upshot is that the dark matter is NOT baryonic matter. It is usually though to be an exotic dark matter particle, but maybe it is primordial black holes.
We illustrate Big Bang nucleosynthesis and the comparison with observed cosmic composition in the figure below (local link / general link: big_bang_nucleosynthesis.html).
Let us summarize the strongest evidence for Big Bang cosmology:
The clouds are at cosmological redshift z = 3.
The clouds constituent another verification of Big Bang cosmology.
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).
These ages are less than the age of the observable universe = 13.797(23) Gyr (Planck 2018) given by the Λ-CDM 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).
And this has really been so since 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 tells us what happened before the Big Bang for example.
We take take up the limitations of the Λ-CDM model (which incorporates Big Bang cosmology) in the following section Limitations of the Λ-CDM Model.
Inflation is the name for a super-rapid exponential expansion phase (cosmic time maybe 10**(-36)--10**(-33) or 10**(-32) s measured from the fiducial time zero of Friedmann equation (FE) models) from a tiny piece of space that may have happened in the very early universe (cosmic time t <∼ 10**(-12) s). The expansion is much more rapid than in the (post-very-early-universe) FE models (i.e., a model with "radiation", "matter", and dark energy whose simplest form is the cosmological constant which is NOT really an energy at all).
After inflation, the cosmic evolution is supposed to track into one of these FE models. See the cartoon of an inflation region growth in the figure below (local link / general link: inflation_region_cartoon.html).
The false vacuum and the inflaton are explicated in the figure below (local link / general link: inflation_false_vacuum_decay.html).
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). For Alan Guth (1947--), see the figure below (local link / general link: alan_guth.html).
Since 1979, the inflation paradigm has evolved quite a bit and has indeed spawned a quasi-infinity of inflation theories.
Among these inflation theories is eternal inflation which, in fact, has many versions itself. We discuss eternal inflation below in subsection Eternal Inflation
The main developer of the theory of eternal inflation is Andrei Linde (1948--): see the figure below (local link / general link: andrei_linde.html).
Inflation was and is considered a good idea just because it offers explanations for three problems.
Alan Guth's (1947--) 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: Alan Guth originally estimated about one MAGNETIC MONOPOLE in the observable universe (Ov-245).
Problem solved---if it ever really existed.
However, even if the magnetic-monopole problem turns out to be a myth, it was useful in furthering research in cosmology.
The temperature of CMB is extremely uniform. It shows fluctuations of only about 1 in 10**5 (see Wikipedia: Cosmic microwave background radiation: Features) after subtracting off the CMB dipole anisotropy due to the Doppler effect caused by the Earth's motion relative to the local comoving frame.
This implies that the whole early universe (cosmic time (10**(-12) s -- 377700(3200) Jyr) before the recombination era t = 377,770(3200) Jyr = 1.192*10**13 s (z = 1089.80(21)) was very homogeneous and in very nearly in exact thermodynamic equilibrium (i.e., at nearly the same temperature).
But in FE models with a Big Bang, points on opposite sides of sky from which CMB flux originated were never CAUSALLY CONNECTED (except perhaps in a limiting sense at that the physically indeterminate and very probably unreal 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---which is explicated in the figure below (local link / general link: horizon_problem.html).
The observable universe has Omega very close to 1: the best available measurements give |Omega -1| = 0.0005(40) (which is consistent with zero with in 1 standard deviation (1 σ)) for the present epoch (Planck 2018 results. I. Overview and the cosmological legacy of Planck 2018, p. 31).
In FE models with Lambda=0, the density parameter Ω(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 instability is illustrated in the figure below (local link / general link: problem_flatness_problem.html).
|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 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 Λ 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 pocket universe 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.
If those models turn out to be essentially wrong, then the observations that lead to Omega very close 1 may have to be interpreted differently and the real Omega may NOT be very close to 1.
And this may actually be the case. A measurement result from strong gravitational lensing suggests that the observable universe is a positive curvature universe (Qi et al. 2018) and Omega is NOT very close to 1.
The flatness problem would disappear if there is NO flatness. In this case, the predicition of flatness for inflation becomes a problem for inflation since it predicts extreme flatness. It will be very exciting if the observable universe is a positive curvature universe. The inflation paradigm may fall. But it's very premature to think that likely circa 2018.
These solutions are general to most INFLATION MODELS.
A main problem with inflation is that there are tens of different INFLATION MODELS.
Which one if any is 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.
Inflation is a paradigm in jargon of philosopher of science Thomas Kuhn (1922--1996).
It's NOT a single well-defined theory.
It's an overall framework for theories.
Inflation, by the by is a framework or paradigm embedded in the grander paradigm of quantum field theory.
Therefore, it is part of what we call quantum cosmology.
Here yours truly 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).
Eternal inflation is one of the most popular inflation theories.
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 universe, 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 (the "acorn") can cause the inflaton to fall into a low energy state or true vacuum. For an acorn, see the figure below (local link / general link: multiverse_acorn.html).
Unlike the a true constant dark energy effect or cosmological constant, the energy of the inflaton varies in time and, in fact, exhausts itself during inflation.
For a cartoon of the false vacuum decay in the inflation era, see figure below (local link / general link: inflation_false_vacuum_decay.html).
The numbers associated with inflation are quite uncertain because no one knows the exact properties 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.
From the figure below (local link / general link: inflation_region_cartoon.html), you can see our pocket universe may have started out as a microscopic speck---albeit one with the all the energy needed to make the huge space we live in.
There is no right answer.
But answer 3 is what many people think is plausible.
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 general relativity and 2nd law of thermodynamics are taken to be general. Without these concepts, we would have little guidance for understanding the multiverse.
Most other pocket universes 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 pocket universe may be explicable by invoking the anthropic principle. But anthropic principle arguments are often hard to make absolutely convincing although they often seem plausible (see IAL 0: A Philosophical and Historical Introduction to Astronomy: The Anthropic Principle).
Philosophically, eternal inflation is satisfying to many people: 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 CANNOT find any evidence that he did.
Philosopher of science Karl Popper (1902--1994) posited as a scientific principle that a scientific theory should be subject to falsification: there should be tests that if the theory fails it is falsified: i.e., wrong, NOT true.
The idea of falsification goes back at least to Blaise Pascal (1623--1622):
Now some argue that the multiverse CANNOT be falsified.
But, in fact, the multiverse keeps passing one significant falsification test as point out by Martin Rees (1942--) (in an article I CANNOT now locate) and probably others. We have already discussed the falsification test above in our discussion of eternal inflation in the cartoon of the eternal inflation in the figure above (local link / general link: inflation_eternal.html).
But to recapitulate the discussion of the falsification test:
This has be debated too, but majority view is willing to concede it yours truly thinks.
See: Shannon Hall, 2015, SciAm, "Thank Your Lucky Constants" , Tim Maudlin, 2013, Aeon, "The calibrated cosmos", S. Borsanyi et al., 2015, Science, "Ab initio calculation of the neutron-proton mass difference", Luke A. Barnes, Geraint F. Lewis, 2017, ArXiv, "Producing the Deuteron in Stars: Anthropic Limits on Fundamental Constants", Luke A. Barnes, 2011, ArXiv, "The Fine-Tuning of the Universe for Intelligent Life".
Answer: Because we're the lucky winners.
This is a plausible argument, but is the multiverse falsifiable? Yes.
If it were over-fine-tuned, then there would be some absolute physical logic/necessity that dictates the observable universe to which life as we know it is an irrelevant accident.
But what if the mass difference were exactly 1/700 = 0.001428571 ... ≅ 0.00143? This is more fine-tuned than is needed for a biophilic observable universe.
There must be some absolute physical logic/necessity that dictates that the neutron-proton mass ratio be exactly 701/700.
Absolute physical logic/necessity would have to be really weird if 701/700 were required.
Folks would really be scratching their heads.
By the way, the ratio is NOT 701/700 to within uncertainty.
So if you require falsifiability for a scientific theory, the multiverse does have it and so far it is NOT falsified.
Actually, it's passed all the simple ratio ones already I think. Well maybe it failed 3 spatial dimensions!!!! But if string theory is right, maybe it passed that one too.
Maybe NOT. Maybe our view of the universe is too superficial to reach that point.
Our occasional UNLV colleague Mario Livio as weighed in: see Livio, M. 2013, How Can We Tell If a Multiverse Exists?
How well supported is the idea of inflation?
It remarkably predicted Omega equal to 1 to within 1 in 10**5 (CL-155) long before observations gave Omega=1.0005(40) (Planck 2018 results. I. Overview and the cosmological legacy of Planck 2018).
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.
Yes. See the figure below (local link / general link: cmb_power_spectrum.html).
The upshot is that the inflation paradigm has some strength and has increased in strength with time: it hasn't simply gone away as some hot concepts do.
But on the other hand, the non-uniqueness problem of inflation makes me wonder if it is the geocentric model epicycle theory of our time.
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 (a modern version of the cyclic 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.
One can cite a representative sample of the major innovations:
The advent of the James Webb Space Telescope (JWST, 2021--2041?) and other new programs and instruments: e.g., Euclid (2023--).
Are more changes are coming?
Well, very probably yes, although Big Bang cosmology as far as it goes seems robust.
Here are some questions:
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 (c.1992--).
Form groups of 2 or 3---NOT more---and tackle Homework 30 problems 15--20 on cosmology, the Λ-CDM model Big Bang cosmology, and inflation cosmology.
Discuss each problem and come to a group answer.
Let's work for 5 or so minutes.
The winners get chocolates.
See Solutions 30.