History of Cosmology

Sections

1. Abstract
2. Introduction
3. Mythological Cosmology and the Flat Earth
4. Hesiod's Cosmogony
5. Parmenides and the Round Earth
6. The Cosmology of the Atomists
7. Aristotelian Cosmology
8. Aristarchos of Samos (c.310--c.230 BCE)
9. The Ptolemaic System
10. The Middle Ages in Western Eurasia
11. The Copernican Revolution
12. The Newtonian Universe c.1650--c.1920
13. The Discovery of Galaxies
14. The Friedmann Equation Models and the Expansion of the Universe
15. The Big Bang Theory
16. The Λ-CDM Model
17. Inflation Cosmology
18. Missions of the 2020s--2030s
19. Conclusion

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Abstract

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We trace the history of cosmology (physical cosmology, not mythical cosmology) from ancient Greek astronomy (c.700 BCE--c.400 CE) to the present circa 2023. We touch on the spherical Earth theory (c.500 BCE), Aristotelian cosmology (c.350 BCE), the Ptolemaic system (c.150 CE), the Copernican heliocentric solar system (1543), the Newtonian Universe (including absolute space, 1687--c.1920), the discovery of galaxies, general relativistic cosmology (more precisely the Friedmann equation models,1917--), the expansion of the universe (c.1920s), Hubble's law (1929), the primeval atom theory (c.1933), Big Bang cosmology (1946--), the Lambda-CDM model (c.1995--), inflation cosmology (c.1979--), and multiverse cosmology (c.1980s--).

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Introduction

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1. Let's just begin.
2. For the full captions for the figures and the credits, just click on the figures.

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Mythological Cosmology and the Flat Earth

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1. flat Earth, dome of sky, underworld.
   
2. Greeks,Norse,probably all other early societies.
   



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Hesiod's Cosmogony

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Hesiod's cosmogony in Hesiod's Theogony (c.700 BCE):


In truth at first Chaos came to be, 
but next wide-bosomed Earth, 
the ever-sure foundation of all the deathless ones 
who hold the peaks of snowy Olympus, 
and dim Tartarus in the depth of the wide-pathed Earth, 
and Eros (Love), fairest among the deathless gods, 
who unnerves the limbs and overcomes the mind and wise counsels 
of all gods and all men within them. 
From Chaos came forth Erebus and black Night; 
but of Night were born Aether and Day, 
whom she conceived and bore from union in love with Erebus. 
And Earth first bore starry Heaven, equal to herself, 
to cover her on every side, 
and to be an ever-sure abiding-place for the blessed gods. 
And she brought forth long hills, 
graceful haunts of the goddess Nymphs who dwell 
amongst the glens of the hills. 
She bore also the fruitless deep with his raging swell, 
Pontus, without sweet union of love.  

Translation: Hugh G. Evelyn-White (1874--1924). See Perseus Digital Library: Hesiod's Theogony, line 104--

1. More like forces and bodies that psychological beings in this brief cosmogony.
2. So as earlier as c.700 BCE, Hesiod (fl. 700 BCE) at least briefly waxed philosophical.



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Parmenides and the Round Earth

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1. Parmenides of Elea (early 5th century BCE) may have proposed the spherical Earth theory first.
2. He gave a philosophical argument, but he probably understood empirical arguments too: Earth's Earth's umbra on the Moon is always round, etc.
3. According to Plato (428/427--348/347 BCE), Socrates (c.469--399 BCE) had heard of the Socrates (c.469--399 BCE) and been persuaded of it (Furley 1987, p. 55).



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The Cosmology of the Atomists

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1. Leucippus (first half of 5th century BCE) and Democritus (c.460--c.370 BCE), the atomists.
2. They were flat Earthers, but posited an infinite, eternal space full of atomist atoms.
3. The atomist cosmology CANNOT be fully known since only fragments of their writings remain. The cartoon below is an attempt at an explication.
4. The atomist cosmology is a vague anticipation of eternal inflation.



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Aristotelian Cosmology

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1. Aristotelian cosmology.
2. Except for the spherical Earth nothing is right.
3. But in western Eurasia, it had a long vogue: circa 350 BCE to circa 1600 CE.
4. There were invisible nested celestial spheres on which the historical planets were carried. The outermost of these was the celestial sphere which was a solid thing on which the stars were pasted and which whipped around us once per day on the celestial axis.
5. Aristotelian cosmology was qualitative. You could NOT calculate ephemerides from it.
6. Aristotelians believed Aristotelian cosmology was physically correct, but only approximately. Nature was too complicated for it to be used for calculations.
7. Being a bit satiric, Aristotelian cosmology is social constructivism in action---the Aristotelians agreed on it, and so it was truth.



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Aristarchos of Samos (c.310--c.230 BCE)

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1. NOT long after Aristotle (384--322 BCE), Aristarchos of Samos (c.310--c.230 BCE) became the first person in recorded history to propose heliocentrism: historical planets (i.e., Mercury ☿, Venus ♀, Mars ♂, Jupiter ♃, Saturn ♄), NO counting the Sun ☉ and Moon ☽ orbited the Sun ☉.
2. But why did Aristarchos of Samos (c.310--c.230 BCE) propose this idea? Probably for the same reasons as Nicolaus Copernicus (1473--1543) about 18 centuries later.
3. Unfortunately, all we have is a few statements telling us Aristarchos of Samos (c.310--c.230 BCE) proposed heliocentrism. NO arguments for heliocentrism or detailed model of his ideas have survived.
4. Nicolaus Copernicus (1473--1543) justly gets the credit for heliocentrism because he gave arguments for it that were unignorable.



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The Ptolemaic System

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Ptolemy (c.100--c.170 CE), the great mathematical astronomer of Greco-Roman Antiquity (see also Wikipedia: Greco-Roman World).



1. A cartoon of the geocentric solar system model the Ptolemaic system of Ptolemy (c.100--c.170 CE).
2. It is an epicycle model.
3. Unlike Aristotelian cosmology, the Ptolemaic system was mathematical astronomy. It could be used to calculate ephemerides.
4. About the ordering of the historical planets (i.e., the Moon ☽, Mercury ☿, Venus ♀, Sun ☉, Mars ♂, Jupiter ♃, Saturn ♄), Ptolemy (c.100--c.170 CE) argued if the outer historical planets moved at the same speed in space then if they move slower in the sky, then they are farther away.
   a reasonable argument and it gives correct answers insofar as they can be correct in the incorrect geocentric solar system model.
5. But no one knew how far the historical planets were or their ordering.
6. Except the ancient Greek astronomers knew the Moon was ∼ 60 Earth radii away from the Earth.
7. A key point about epicycle models is they are vastly non-unique. You can make many versions and they will all give you approximately the same ephemerides. For ∼ 13 centuries in western Eurasia, people tried all kinds of versions.
8. The non-uniqueness problem suggested epicycle models were just NOT true and strict Aristotelians argued this.



Now Ptolemy (c.100--c.170 CE) mostly followed Aristotelian physics in many respects, but the Ptolemaic system is NOT consistent with Aristotelian cosmology, and so western Eurasia was stuck with two geocentric solar system models:

1. Aristotelian cosmology which Aristotelians argued was essentially physically real, but qualitative and so could NOT be used calculate ephemerides because nature was too complex.
2. Ptolemaic system which could be used to calculate ephemerides, but according to Aristotelians was just a calculating tool---which is true.

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The Middle Ages in Western Eurasia

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The ancient Greek astronomers had many of the ingredients for great advances in astronomy and cosmology:

1. the spherical Earth.
2. atomism and the infinite universe, but as a minority view.
3. the heliocentric solar system, but as very minority view.
4. mathematical astronomy.

But the ancient Greek astronomers did NOT put the pieces together and neither did the Medieval astronomers.

But many advances were made in the Middle Ages in western Eurasia:

1. Arabic numerals.
2. algebra.
3. trigonometric functions: see Wikipedia: History of trigonometry: Medieval Islamic world.
4. observations: see Medieval Islamic observatories.

But in theoretical astronomy, western Eurasia was stuck in the mire of the double astronomy of Aristotelian cosmology (see Aristotelian cosmology cartoon) and the Ptolemaic system (see Ptolemaic system cartoon).

13 centuries of wheel spinning.



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The Copernican Revolution

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1. Nicolaus Copernicus (1473--1543): maybe a self-portrait or based on one.

   

2. One diagram shows you why Nicolaus Copernicus (1473--1543) posited heliocentric solar system.

   

3. Nicolaus Copernicus's (1473--1543) own Copernican system not-to-scale.

   

4. Thomas Digges' (c.1546--1595) and the return of the infinite (or quasi-infinite) universe:
   1. After Thomas Digges (c.1546--1595), the development of the Copernican system is really history of the knowledge of Solar System, NOT cosmology per se.
   2. So yours truly will NOT detail the history of Copernican Revolution: Tycho Brahe (1546--1601), Galileo (1564--1642), Johannes Kepler (1571--1630), etc.

   

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The Newtonian Universe c.1650--c.1920

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1. Newtonian physics explicated the Solar System and in the thinking of Isaac Newton (1643--1727) and most of his contemporaries the Solar System was embedded in a universe of stars which probably had their own planetary systems.

   Isaac Newton (1643--1727) only speculated a little and inconclusively on the structure of the universe and what held it up against self-gravity.

   

2. Isaac Newton (1643--1727) presented in his book the Principia (1687): Newton's 3 laws of motion, Newton's law of universal gravitation, etc.

   By the way, the Principia (1687) is an awful book.

   

3. But there was a problem with a universe of stars: Olbers' paradox which was known long before Heinrich Wilhelm Matthias Olbers (1758--1840) and was explicated by none other than Edmond Halley (1656--1742) directly to Newton himself at a meeting of the Royal Society.

   Olbers' paradox is strong evidence against an infinite, eternal, static universe full of stars.

   

4. The universe of stars, full or NOT, had another aspect:
   1. The stars were NOT spread uniformly throughout space, infinite or NOT. They were somewhat concentrated into the Milky Way
   2. 18th century speculators posited that the Milky Way was disk of stars held up by rotation around a center of mass and the Sun was embedded in this disk. This is, of course, absolutely correct.
   3. Below is an all-sky sky map showing the Milky Way which you CANNOT see in Las Vegas, Nevada because of all the light pollution---recently added to by the Las Vegas Sphere (formally Sphere at The Venetian Resort)---which can be used as a giant celestial globe, so who needs the night sky. Yours truly wishes he had a button that could turn off the Las Vegas Strip for an hour or so during lab time.

   

5. William Herschel (1738--1822):

   

   1. William Herschel (1738--1822) followed up the idea of the Milky Way as a disk by mapping it with star gages.

      It was a great idea, but he was defeated by interstellar dust.

   2. William Herschel (1738--1822) is famous for discovering Georgium Sidus which we call Uranus ⛢,♅.

      And he was a composer: William Herschel (1738-1822) - Symphony No 12 in D Major, 2nd movement 4:26--11:30.

   3. William Herschel's (1738--1822) map is below which is a cross section of the Milky Way, or so yours truly guesses.

   

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The Discovery of Galaxies

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How did we discover there were other galaxies other than the Galaxy (AKA Milky Way)?

1. In recorded history, knowledge of the nebulae (historical usage) goes back to Ptolemy (c.100--c.170 CE).

   

2. But, of course, Ptolemy (c.100--c.170 CE) did NOT know of the most prominent nebulae (historical usage) the Magellanic Clouds (i.e., Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC)).

   

   

3. That the nebulae (historical usage) as other galaxies was guessed at fairly early in the post Copernican Revolution era by none other than Sir Christopher Wren (1632--1723) more famous as an architect, than as an astronomer:
   Sir Christopher Wren
   Said, "I am going to dine with some men.
   If anyone calls
   Say I am designing St. Paul's.
   
   ----a clerihew by Edmund Clerihew Bentley (1875--1956).

   Sir Christopher Wren's (1632--1723) speculation:

   ... a Time would come, when Men should be able to stretch out their Eyes as Snails do, & extend them to fifty feet in length; by which means, they should be able to discover Two thousand Times as many Stars as we can; and find the Galaxy (i.e., Milky Way) to be Myriads of them; and every nebulous Star appearing as if it were the Firmanment of some other World, at an incomprehensible Distance, bury'd in the vast Abyss of intermundious Vacuum ...
   ---1657 quotation from Robert I McLachlan 2019, arXiv:1909.02167, p. 3.

   Sir Christopher Wren's (1632--1723) speculation had NO historical impact, but shows even before Newtonian physics that at least someone could speculate on a universe full of galaxies in addition to one full of stars.

   Others in the 18th century speculated on other galaxies: the architect Thomas Wright (1711--1786), the philosopher Immanuel Kant (1724--1804), the mathematician Heinrich Lambert (1728--1777), and William Herschel (1738--1822).

4. In the 19th century, we come to Lord Rosse (1800-1867)---who may have believed in other galaxies.

   

5. Lord Rosse (1800-1867) built the largest telescope up to his time the Leviathan of Parsonstown (1.83 m = 6 ft, operational 1845--c.1890).

   

6. The discovery of the spiral nebulae (i.e., that some nebulae (historical usage) had spiral structure) by Lord Rosse (1800-1867) using the Leviathan of Parsonstown (1.83 m = 6 ft, operational 1845--c.1890).

   Below is Lord Rosse's (1800-1867) drawing from visual astronomy of the Whirlpool Galaxy (AKA M51a/NGC 5194 and M51b/NGC 5195) in constellation Canes Venatici in 1845.

   

7. Below is a modern image of Whirlpool Galaxy (AKA M51a/NGC 5194 and M51b/NGC 5195).

   Qualitatively, Lord Rosse (1800-1867) didn't do too badly.

   

   

8. Edwin Hubble (1889--1953) discovered in 1924 (see Wikipedia: Edwin Hubble: Universe goes beyond the Milky Way galaxy) that the spiral nebulae were other galaxies, and so, of course, were the elliptical nebulae since they were found in galaxy clusters with spiral nebulae.

9. Hubble tuning fork diagram which Edwin Hubble (1889--1953) invented in 1926 shortly after discovering the extragalactic nature of the nebulae (historical usage).

   It classifies spiral galaxies, elliptical galaxies, lenticular (S0) galaxies, and irregular galaxies.

   

10. Edwin Hubble's (1889--1953) discoveries were predicted on having the best telescope in the world in the 1920s when southern California was a great observing site.

    

11. Edwin Hubble's (1889--1953) discovery was made by determining the distance to the Andromeda Galaxy (M31, NGC 224) using Cepheid variables:
    1. He reported in 1924, Hubble had established the distance to the Andromeda Galaxy (M31, NGC 224) to be 285 kpc (No-510).

    2. This is NOT a very accurate result. Hubble had various systematic errors in his measurements and calibrations that are entirely understandable given his time.

    3. The modern distance to the Andromeda galaxy is about 725 kpc (Cox-578): this ∼ 2.5 times Edwin Hubble's (1889--1953) value.

    4. But even if Hubble's contemporaries suspected large errors---and they may have---they did concede??? that the Andromeda galaxy had to be a remote large system of stars comparable in size to Milky Way.

       It's ironic to think that an extremely important true result was accepted as such while unknown large systematic error weakened original evidence on which it was accepted.

    5. The observable universe was a universe of galaxies. Edwin Hubble's (1889--1953) entitled his famous book The Realm of the Nebulae (Edwin Hubble, 1936, Google Books, partially online) (see also The Realm of the Nebulae (Edwin Hubble, 1936, NASA/ADS); No-509).

    6. Edwin Hubble's (1889--1953) remained old-fashioned in that he continued to call galaxies nebulae (historical usage).

    

12. The Virgo Cluster where spiral galaxies and elliptical galaxies are found together which proved that if spiral nebulae were galaxies that elliptical nebulae were also galaxies.

    

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The Friedmann Equation Models and the Expansion of the Universe

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1. Albert Einstein (1879--1955) in his prime.

   

2. The Einstein universe (1917): finite, unbounded cosmological model with the geometry of the surface of 4-dimensional Euclidean space sphere: i.e., a 3-N hypersphere.

   

   EOF

   To find the Einstein universe (1917), by the klutzy means available in those early days of general relativity, Albert Einstein (1879--1955) invented the cosmological constant Λ:
   1. cosmological constant Λ is an extra term in the Einstein field equations that only has an effect on the cosmological scale, and so does not affect any of the other results of general relativity.

   2. By klutzy means, we mean Albert Einstein (1879--1955) did NOT have the Friedmann equation (FE, 1922). If he had discovered the Friedmann equation (FE, 1922) himself, his work in cosmology would have been vastly easier.

      Einstein universe (1917) is, in fact, a Friedmann-equation (FE) model discovered without using the Friedmann equation (FE, 1922).

   3. Albert Einstein (1879--1955) adjusted the cosmological constant Λ to make the Einstein universe (1917) static.

   4. In fact, Albert Einstein (1879--1955) was NOT trying to create a cosmological model of full realism which he new was far too ambitious for 1917.

   5. What he was trying to do was show that a cosmological model consistent with general relativity could be found.

   6. General relativity was posited as a univeral theory.

      For this to be true, general relativity had to apply to the universe as whole.

      Newtonian physics does NOT do this without extra hypotheses.

   7. Of course, Albert Einstein (1879--1955) thought he needed one extra hypothesis too: the cosmological constant Λ.

   8. In fact, he did NOT need it as Alexander Friedmann (1888--1925) would show---if you allow for expanding universe or a contracting universe.

3. Willem de Sitter (1872--1934), de Sitter universe (1917), and the cosmic scale factor a(t).
   1. Willem de Sitter (1872--1934) discovered de Sitter universe (1917) also in 1917 which is also, in fact, a Friedmann-equation (FE) model discovered without using the Friedmann equation (FE, 1922).

   2. The de Sitter universe (1917) is an exponentially expanding Friedmann-equation (FE) model with NO matter and NO electromagnetic radiation (EMR).

      It just has the cosmological constant Λ.

      It is also infinite and eternal---it's been expanding emptily forever and always will.

      But the de Sitter universe (1917) did predict the expanding universe and the cosmological redshift.

      It also predicted Hubble's law, but no one seems to have noticed that explicitly.

   3. What is the expanding universe in Friedmann-equation (FE) models?

      In the ideal, Friedmann equation (FE) model, all lengths scale with cosmic time by the cosmic scale factor a(t):

          r(t) = a(t)*r_0   

      where 0 symbolizes cosmic present = to the age of the observable universe = 13.797(23) Gyr (Planck 2018).

   

   

4. Alexander Friedmann (1888--1925) and the Friedmann equation (1922).

   The Einstein universe (1917) and de Sitter universe (1917) are Friedmann equation (FE) models discovered by klutzy means before the discovery of the Friedmann equation (1922).

   What is the Friedmann equation (1922)?

   The Friedmann equation (1922) describes the dynamics of the universe as whole.

   1. It is derived from general relativity. with simplifying assumptions about what the universe.
   2. The universe is homogeous and isotropic.
   3. The universe has no boundary in space though it may have in time.
   4. All matter, electromagnetic radiation (EMR), or any other mass-energy can be modeled as perfect fluids.
   5. The independent variable is time.
   6. The dependent variable is the cosmic scale factor a(t).
   7. The Friedmann equation (1922) is an ordinary differential equation. But it is nonlinear differential equation with only a limited set of analytic solution.
   8. The Einstein universe (1917) is the only static solution to the Friedmann equation (1922): all other solutions are expanding or contracting.
   9. Alexander Friedmann (1888--1925) used the Friedmann equation (1922) find some Friedmann equation (FE) models: i.e., cosmic scale factor a(t).
   10. Unfortunately, Alexander Friedmann (1888--1925) published in Russian no one much outside of Russia knew about his work until several years later by which time he had passed away.

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

   Lemaitre independently discovered the Friedmann equation (1922) in 1927. None other than Albert Einstein (1879--1955) informed him that it was a rediscovery in 1927 (see MacTutor: Georges Lemaitre (1894--1966)).

   However, Lemaitre explicitly discovered (as Alexander Friedmann (1888--1925) did NOT) Hubble's law as a necessary consequence of the Friedmann equation (1922).

   This was a theoretical discovery of a consequence of the Friedmann equation (1922), NOT an empirical discovery that the observable universe obeyed Hubble's law.

   However, Georges Lemaitre (1894--1966) did deduce a value for the Hubble constant based on published data that was only somewhat worse than Edwin Hubble (1889--1953) own value from 1929.

   But this was NOT a proof that Hubble's law applied to the observable universe.

   No one much noticed Georges Lemaitre (1894--1966) work in 1927 since he published in French and was published only in the obscure Annals of the Scientific Society of Brussels.

   Except Albert Einstein (1879--1955)---who didn't think much of it at that time.

6. Hubble's law was empirically discovered by Edwin Hubble (1889--1953) in 1929.

       v=Hr   

   which holds for every instant in cosmic time in Friedmann equation (FE) models.

   

   Hubble's value for the Hubble constant was really bad: i.e., ∼ 500 (km/s)/Mpc.

   This suggested a characteristic age for the observable universe of order 2 billion years.

   But circa 1930, the Earth was already known to be of order 3 billion years from radioactive dating.

   So there was an AGE PROBLEM which was only finally resolved when the Hubble constant was revised to 50--100 500 (km/s)/Mpc after circa 1950.

7. Now most Friedmann equation (FE) models imply a point origin for the observable universe which we now call Big Bang singularity.

   In the 1930s, most cosmologists---of whom there were maybe 10---thought nothing of this.

   But Georges Lemaitre (1894--1966) presented his primeval atom origin in 1931--1933 which is a "cold big bang theory" as a part of what we can call the the Lemaitre universe (1933)---an ingenious theory that turned out to be wrong---and probably did NOT excite as much interest as it should have had in the 1930s.

   The Lemaitre universe (1933):

   1. In the earliest time traceable (but NOT the beginning of time), the universe was a giant "neutron star" (i.e., the primeval atom itself) that filled a finite, unbounded 3-N hypersphere. So an actual point origin was avoided.
   2. It was expanding and decelerating initially.
   3. The primeval atom fragmented into smaller atoms by radioactive decay: "nuclear fission", but NOT our nuclear fission which was discovered in (see Wikipedia: Nuclear fission: Discovery of nuclear fission; Wikipedia: Discovery of nuclear fission).
   4. There was a nearly zero growth phase (Einstein universe (1917) phase) which could be as long as needed by adjusting the cosmological constant Λ. This avoided the AGE PROBLEM of the 1930s.
   5. In the Einstein universe (1917) phase, gravitational collapses occurred leading to galaxies and stars which were powered by radioactive decays.
   6. After the Einstein universe (1917) phase, the universe began to exponentially expand and became the expanding universe we observe.
   7. The expanding universe is in de Sitter universe (1917) phase.

   

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The Big Bang Theory

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1. George Gamow (1904-1968) proposed and the Big Bang theory (a "hot big bang") in its earliest form in 1946 (see Wikipedia: Big Bang: Concept history; Wikipedia: History of the Big Bang theory; Gamow, G. 1946, Physical Review, 572--573, Expanding Universe and the Origin of the Elements).

   George Gamow (1904-1968) and his colleages Ralph Alpher (1921--2007) and Robert Hermann (1914--1997) (who knew a lot more about nuclear physics than the other George---Georges Lemaitre (1894--1966) proposed for near the mythical point origin:

   1. A hot phase rich in photons with a relatively small amount of mass-energy in the form of matter.

   2. He proposed that ALL the elements of the observable universe were synthesized in this hot early phase of expanding universe by nuclear fusion This is what came to be called the Big Bang.

   3. The expansion of the universe caused adiabatic cooling and turned off the Big Bang nucleosynthesis era (cosmic time ∼ 10--1200 s ≅ 0.17--20 m in modern theory).
   4. Gravitational collapses occurred leading to galaxies and stars which were powered by nuclear fusion.

   5. The cosmic background radiation (CBR) left over from the Big Bang also adiabatic cooled and became the modern cosmic microwave background (CMB).

   6. Ralph Alpher (1921--2007) and Robert Hermann (1914--1997) predicted the cosmic microwave background (CMB) and predicted its temperature would be ∼ 5 K. Their predicted temperature is fortuitously close to the modern value CMB temperature T=2.72548(57) K. Their calculation was actually NOT right (see Mike Turner 2021, Predicting the CMB temperature).

   

2. A log-log plot cosmic temperature versus cosmic time from the quark era (cosmic time t∼ 10**(-12) -- 10**(-6) s) to the recombination era t = 377,770(3200) Jyr. Time zero is the Big Bang singularity which probably did NOT happen. Our best theory is that the inflation era (10**(-36) -- 10**(-32) s) happened in the very early universe (t < 10**(-12) s) and then the universe tracked into a standard Friedmann-equation model thereafter.

   

3. Big Bang nucleosynthesis era (cosmic time ∼ 10--1200 s ≅ 0.17--20 m):
   1. By the 1960s, it became clear that only the observable universe's hydrogen (H), helium (He) (mostly), and some of its lithium (Li) were synthesized in the Big Bang nucleosynthesis era (cosmic time ∼ 10--1200 s ≅ 0.17--20 m).

      They is unbelievable, but so is the universe.

   2. All other elements were synthesized in stars and supernovae---except for trace amounts of some rare isotopes which are synthesized in rare processes.

   
4. The cosmic composition results from the Big Bang and then stars and supernovae.

   

5. The nearly perfect blackbody spectrum of the cosmic microwave background (CMB) from the Cosmic Background Explorer (COBE, 1989--1993).

   The cosmic microwave background (CMB) is one of the strongest proofs of the Big Bang theory: there is NO other plausible explanation for cosmic microwave background (CMB) given all the other constraints of the observable universe.

   The cosmic microwave background (CMB) was discovered fortuitously in 1965 by Arno Penzias (1933--) and Robert Wilson (1936--).

   

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The Λ-CDM Model

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1. From 1930s to the 1990s various cosmological models had vogues including the Lemaitre universe (in the period before circa 1965 but without primeval atom) and the Einstein-de Sitter universe (1932) (in the period circa 1965--circa 1995).

2. From the circa 1995, the vogue model has been the Λ-CDM model: the current standard model of cosmology (SMC, Λ-CDM model), but it is now under attack from tensions.

   

3. The Lambda-CDM model cosmic scale factor a(t), the cosmic temperature, and the approximation ionization until the recombination era, z=1089.90(23), t=377,700(3200) years).

   

4. Words for our ignorance dark matter (the cold dark matter or CDM) and dark energy (the alternative to the cosmological constant Λ).

   Dark matter:

   1. Dark matter is ∼ 6 more abundant than ordinary matter baryonic matter.

   2. The dark matter clumped in the early observable universe to form dark matter halo in which the galaxies formed. The baryonic matter was clumped by the gravitational force of the dark matter

   3. The amount of dark matter in galaxies is ∼ 10--30 ??? times more than the baryonic matter as we know from galaxy rotation curves.

   4. What is the dark matter? The standard idea is that is an exotic particle that is highly non-interacting with itself and other matter, except through gravity. The exotic particle forms a pressureless gas.

   5. So far the dark matter has NOT been observed directly. Its exitence has been inferred from its gravitational effect.

   6. There are endless theories about what the exotic particle is and there are very advanced searches for it---that have had NO luck so far.

   

   Dark energy:

   1. Since circa 1998, we know that the universal expansion has been accelerating, NOT decelerating as in the Einstein-de Sitter universe (1932).

   2. The easiest theoretical solution has been the cosmological constant Λ adjusted to give acceleration rather than a static Friedmann-equation (FE) model. Hence the &Lambda in the term Λ-CDM model.

   3. However, cosmological constant Λ can be replaced by a (constant) dark energy which has the same cosmological effect as the cosmological constant Λ, but differs in other respects.

   4. Now particle physicists favor dark energy for darn good particle physics reasons---but they can't tell us what it should be exactly.

   5. In fact, cosmologists tend to just conflate cosmological constant Λ and dark energy as &Lambda when they are just specifying the cosmological effect.

   6. But what is dark energy and does it have to be constant? There is NO end of theories but which if any is right we do NOT know.

   

5. The Hubble tension:
   1. Direct measurements H_0 = 73(2) (km/s)/Mpc (fiducial values).
   2. The indirect measurements based on fits of the Λ-CDM model to observations give H_0 = 67.36(54) (Planck 2018, p. 14).
   3. So >∼ 3 sigma discrepancy.
   4. Uddin et al. 2023 find the tension is less than 3 sigma form local direct measurements, and so there is still an argument about the tension.

   

   

6. Are the tensions going to cause us to change to a new standard model of cosmology (SMC)?

   Very likely, but ...

   It seems almost always case, you see one new paper saying how the Lambda-CDM model fails their test by 3 or 4 sigma and then the next new paper says how the Lambda-CDM model is consistent with their test.

   Obviously, the Lambda-CDM model is just a very good discription of the observable universe to within a few percent loosely speaking.

   Finding a new cosmological model that fits everything to within tenths of a percent and maybe is fundamentally true is a challenge.

   What are the possible new cosmological models?

   They are quasi endless and all over the place.

   Which if any of them are right is a hard question.

   But more data (exabytes of it) is on the way.

   More below on more data.

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Inflation Cosmology

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1. Inflation cosmology describes what came before the Big Bang.

   The inflaton.

   

2. A cartoon of the cosmic scale factor a(t) of observable universe including the inflation era (cosmic time ∼ 10**(-36)--10**(-33) or 10**(-32) s).

   

3. The horizon problem illustrated. The diagram is not-to-scale.

   

4. The Cosmic microwave background (CMB) power spectrum as determined by several experiments indicated on the graph.

   

5. A cartoon of eternal inflation which is both a version of inflation and a version of the multiverse: a universe made up of some kind of pocket universes.

   One assumes general relativity applies to the whole multiverse, and so maybe the multiverse is in overall expansion or contraction.

   But is the gravitational constant G = 6.67430(15)*10**(-11) (MKS units) the same throughout the multiverse?

   

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Missions of the 2020s--2030s

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The new spacecraft missions of the 2020s and 2030s will map out the cosmic scale factor a(t) to better accuracy than now---hopefully much better.

They should also put much tighter constraints on structure formation (AKA large-scale structure formation).

Exabytes of new data will become available.

Alas, all the information will have to be pulled out of the data by statistics.

Ernest Rutherford (1871--1937) once said if you need statistics, you are doing the wrong experiment.

To gloss his aphorism, you should do the decisive experiment.

The information from statistics is all we have it seems.

The new spacecraft missions:

1. Euclid (c.2021--c.2027) videos:
   1. Euclid in a nutshell (2023) | 1:14: The Euclid spacecraft (2023--2029?) and its space mission. Good for the classroom.
   2. The Euclid Space Telescope: tackling dark matter and dark energy mysteries (2023) | 14:54: A good explication of the Euclid spacecraft (2023--2029?) and its space mission. Too long for the classroom.
2. James Webb Space Telescope (JWST, 2021--2041?) videos:
   1. The Emergence of Galactic Structure in the JWST Era CfA Colloquium with Erica Nelson, 2023mar28 | 1:07:00: Probably, good on implications for large scale structure of the observable universe. The new stuff starts at 22:00. Too long for the classroom.
   2. 2023 William H. Pickering Lecture: Discoveries with the James Webb Space Telescope, 2023jan25 | 1:02:56: "William H. Pickering Lecture: Discoveries with the James Webb Space Telescope, featuring remarks by Jonathan Gardner, deputy senior project scientist, James Webb Space Telescope, NASA Goddard Space Flight Center, at the AIAA SciTech Forum in National Harbor, MD, January 25, 2023." Too long for the classroom.
3. Roman Space Telescope (RST, c.2025--c.2030, formerly WFIRST) videos:
   1. NASA's Nancy Grace Roman Space Telescope: Broadening Our Cosmic Horizons | 2:19: From NASA: Nancy Grace Roman Space Telescope. Good for the classroom.
   2. Simulated Image Demonstrates the Power of NASA's Nancy Grace Roman Space Telescope | 2:42: From NASA: Nancy Grace Roman Space Telescope. Too detailed for the classroom.
   3. Nancy Grace Roman and the Roman Space Telescope, 2023jun28 | 1:34:59: On both Nancy Roman (1925--2018) and the mission of her eponymous Roman Space Telescope (RST, c.2025--c.2030, formerly WFIRST). Far too long for the classroom.

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Conclusion

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To conclude:

1. We are in the golden age of cosmology (c.1992--).
2. The cosmic scale factor a(t) will certainly be mapped out better by Euclid (c.2021--c.2027) and the Roman Space Telescope (RST, c.2025--c.2030, formerly WFIRST) by circa 2030.
3. But will cosmology and particle physics solve all their combined mysteries? Maybe soon, maybe never.
4. In any case, it is amazing that from our small platform Earth, we can contemplate eternity and infinity.