COSMOLOGY 

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• Historical Perspective
• Cosmological Facts
• Hubble Law
• Abundances
• Microwave background
• Cosmological Concepts
• Big Bang
• SpaceTime
• Cosmic Horizon
• Critical Density
• Inflationary Cosmology
 

• 1823--Heinrich Olber (German) noted a paradox: in an infinitely large and infinitely old universe the sky would be as bright as the surface of the Sun. This would be so because every direction in the sky would be packed tightly with stars, with no gaps between the stars; thus the sky would be as bright as the surface of a star.  But we observe the sky to be dark at night!

 
• 1848--Interestingly, Edgar Allan Poe (of scary story fame) suggested a way out of this impasse: the universe may be infinitely large but of finite age, in which case since we haven't yet received light from the most distant stars there would be gaps between the visible ones and so the sky could appear dark.

 
• 1916--Einstein published a new theory of gravity, called general relativity. His theory predicted a universe that would either expand or contract depending on the density of matter and energy within it. But, in those days, a dynamic universe was thought to be such a crazy idea that even Einstein could not believe it. Therefore, he modified his theory to make it predict a static universe. Subsequently, Einstein would call this fudging of his equations the biggest mistake of his life.

 
• 1919--The British astronomer Sir Arthur Eddington led an expedition to West Africa to observe a solar eclipse and test Einstein's prediction of the bending of light by the warping of spacetime near the sun. Eddington confirmed Einstein's prediction.

 
• 1922--The Russian mathematician Alexander Friedmann abandoned Einstein's static universe model and worked out the mathematics and geometry of expanding universes. To make progress with the mathematics he made the simplifying assumption that:

 
• the universe is isotropic (looks the same in all directions) from every vantage point, at all times. This implies a universe in which the matter and energy are uniformly distributed.

 
With this assumption (called by Einstein the Cosmological Principle, which earlier Einstein had arrived at on philosophical grounds) and using Einstein's equations of gravity Friedmann constructed a mathematical model that described an expanding universe. The calculations were later repeated by the American Howard Robertson in 1935.
 
• 1924--Edwin Hubble, using work by Henrietta Levitt on Cepheid variables, measured the distance to 9 galaxies and proved that they are very distant.

 
• 1927--Abbe Georges Lamaitre (a Belgian priest) took seriously the idea of an expanding universe. He reasoned that if one went sufficiently far back in time all the matter we see in the universe must have been squeezed into a very small volume, a "Primeval Atom" which subsequently fragmented to form the galaxies and stars we see today. Lamaitre derived a relationship between what later turned out to be Hubble's constant and the age of the universe.

 
• 1929--Drawing on observations made by others as well as his own, Edwin Hubble concluded that the further away a distant galaxy is from us the greater its red shift, Z. The red shift is defined by

 
Z = (lo - le)/le
 
where lo is the observed wavelength on Earth and le is the emitted wavelength at the source. The simplest way to obtain a red shift from the light emitted by an object is to have the object move away from the observer. A light source that moves away from us looks redder, while one that moves towards us looks bluer. This is just the doppler effect.

Hubble therefore made the bold proposal that the observed red shifts was evidence that the galaxies are receding from us, that the universe is expanding, just as Einstein's original equations predicted. Einstein's self-confessed blunder was his initial failure to take seriously this startling prediction.  The velocity at which galaxies recede from us is called the recession velocity. According to the cosmological principle wherever one happened to be in the universe the galaxies would appear to recede from you in the same way. We do not occupy a privileged position; we are not at the center of the universe.

Here is a recent graph of the red shift-distance relationship which is obtained by studying Type Ia supernovae. See also, Supernova Cosmology Project home page.
 

• 1940s--George Gamow (a Russian) and later Ralph Alpher and Robert Herman of Johns Hopkins University refined Lamaitre's idea of a primeval atom. Alpher and Herman reasoned that far back in the past particles of matter would be constantly colliding with each other. These collisions would generate a tremendous amount of heat in the form of photons of very short wavelengths. The temperature would be billions of degrees.

But as the universe expands all length scales are stretched by the expansion. In particular,  the primordial photons would have their wavelengths stretched; that is, the photons would have progressively lower energies and would therefore grow ever colder. Alpher and Herman predicted that the universe should now be bathed in a feeble radiation whose temperature would be just a few degrees above absolute zero. Alas, their ideas were more or less forgotten.
 

• 1965--At Bell Labs in New Jersey, Arno Penzias and Robert Wilson were preparing a radio telescope to observe the Milky Way. They noted a persistent background noise wherever they pointed their telescope. They tried very hard to get rid of it, but couldn't. They had discovered, by accident, microwave photon radiation coming from outer space, that was not associated with any known astronomical objects. This radiation is now called the cosmic microwave background (CMB).

At the same time Bob Dicke and Jim Peebles (at Princeton), working on a suggestion by George Gamow (an ex-student of Friedmann) that the universe might have been hot and dense in the past, were just getting ready to look for the "afterglow" radiation from this dense hot phase of the early universe when they were scooped by Penzias and Wilson. Sadly for Dicke and Peebles it was Penzias and Wilson who got the 1978 Nobel Prize for Physics for their accidental disovery of the microwave background!

• Hubble's Law--For a galaxy a distance d away from us and receding at a speed v we have

 
v = H₀d
where H₀ is Hubble's Constant which is about 65 km/s per megaparsec. That is, for every megaparsec the speed of recession increases by about 65 km/s.
 
• Abundances--The matter in the universe consists largely of hygrogen, helium, deuterium and lithium. The observed proportions of these elements in the universe is

 

Element	Structure	Abundance (%)
Hydrogen	1 proton	77
Helium-4	2 proton, 2 neutrons	23
Deuterium	1 proton, 1 neutron	10-3
Helium-3	2 protons, 1 neutron	10-3
Lithium	3 protons, 4 neutrons	10-8

 
• Cosmic Microwave Background Radiation--This is observed to have a perfect thermal radiation spectrum corresponding to a temperature of 2.7 K. Indeed, it is the most perfect thermal spectrum known. The microwave radiation comes to us from all directions and is observed to be uniform across the entire sky to one part in ten thousand. This is one of the most extraordinary discoveries of our times. See COBE home page.

• The Big Bang--The best current explanation of the cosmological facts is that the universe began a finite time ago in a titanic explosive event, called the Big Bang, which can be called the creation of the universe.

 
• Age of the Universe t--By definition, the age of the universe is the time since the big bang. Suppose we look at a galaxy that is a distance d away from us and let's assume (to keep things simple) that over the age of the universe t the galaxy's recession speed v was constant. The age of the universe can be estimated by finding out how long it has taken the galaxy to move a distance d away from us:

 
t = d/v
 
or, when we use Hubble's Law  v = H₀d ,
 
t = 1/H₀
 
That is, the age of the universe is just the inverse of the Hubble constant. A more accurate calculation must take account of the fact that the gravity arising from all forms of matter and energy in the universe slows down the expansion. This calculation was first performed by the Belgian priest Lamaitre, who obtained:
 
t = (2/3) x (1/H₀)
as the age of the universe. General relativity predicts that a denser universe expands faster than a less dense one. Therefore, a denser universe will expand to a given size sooner than one that is less dense.

One of the first people to determine the age of the universe was Bishop Ussher, who defined the age of the universe as the time since its creation by God. He determined that the universe was created on Sunday, 23 October, 4004 BC. Modern estimates are somewhat earlier than this!

For example, if we take Hubble's Constant to be 50 km/sec per megaparsec we predict an age of about 15 billion years.
 

• Critical Density--Spacetime is made of 3 space plus 1 time dimension--that is, it is a 4-dimensional volume! Moreover, this volume can be warped!

Unfortunately, our human intuition is incapable of imagining such a thing; our understanding of higher dimensions is based upon our intuition about 2-dimensional surfaces. The 4-dimensional volume can curve in different ways depending upon the density of matter in the universe. There are three possibilities:
 

• Open Universe--In this case the global geometry has negative curvature. This is quite impossible to imagine. Negative curvature arises if the matter/energy density is less than a critical value of about 3 Hydrogen atoms/cubic meter. There is then not enough matter to slow down the expansion sufficiently and the universe will expand forever.

 
• Closed Universe--In this case the global geometry has positive curvature. This curvature is akin to the curvature of a sphere. The universe would have a finite volume but no boundary, just like the surface of a sphere. Positive curvature arises if the density is greater than the critical density. Then there is enough matter eventually to halt the expansion and cause the universe to re-collapse in a titanic implosion called (inevitably) the Big Crunch.

 
• Flat Universe--The global geometry has zero curvature, just like the geometry of a flat plane. Flat geometry arises if the density is exactly equal to the critical density. In this case, the universe will expand forever but will just reach a zero expansion speed in the infinite future. Most cosmologists believe the global geometry of the universe is flat.

 
• Cosmic Horizon--How far can we see?

We see the universe because of the radiation that comes to us at the speed of light. So in 15 billion years the maximum distance that the radiation can travel is 15 billion light years. The light from objects further out than 15 billion light years has not had enough time to reach us and so these objects cannot be seen. However, as the universe ages we will be able to see further and further into space. The maximum distance to which we can see, at any given time, is called our Cosmic Horizon. The cosmic horizon defines the Visible Universe. Here is an animation of the big bang.
 

INFLATIONARY COSMOLOGY
 

The Big Bang Theory

• Successes

The big bang theory is able to account for the following facts:

• Universal expansion
• Microwave background radiation
• Abundance of light elements

 
• Problems

It fails to account for:

• Why the microwave background so uniform (Horizon Problem).
• Why the galaxies are distributed in vast sheets (Structure Formation Problem).
• Why spacetime is so flat (Flatness Problem).
• Why there are no monopoles (Monopole Problem).
• How something can be created, apparently, from nothing (Creation Problem).

This theory is a modification of the standard big bang theory. One postulates the existence of a vacuum endowed with a (still mysterious) form of energy. It is mysterious in that the vacuum still looks empty, that is, devoid of ordinary matter and energy. In the beginning, one assumes the vacuum energy density to be huge. This caused the universe to expand at an exponentially fast rate: the universe doubles its size every one trillion trillion trillionth of a second (10^-36 s)! This period of hyper-expansion is called inflation.

The universe is thereby stretched by an absolutely enormous factor, so much in fact that any relatively small region of the universe, for example the entire visible universe, would appear flat, just as a small patch of the Earth's curved surface appears flat. This solves the Flatness Problem.

Any weird things, like monopoles, that may have been created at the start would have been so enormously dispersed that we would expect no more than one in our visible universe! This solves the Monopole Problem. 

What we call the visible universe was once confined to a single bubble no more than 3 x 10^-26 cm across; the distance light can travel in the 10^-36 seconds since the beginning. Therefore, every part of the visible universe was once in contact. This solves the Horizon Problem.

Finally, somehow, after a very short time, the inflation ceases abruptly. It is assumed that the vacuum energy during inflation has been rapidly decreasing. Whatever vacuum energy remains after inflation transforms explosively into ordinary matter and energy, thereby making the universe extremely hot. The regular big bang expansion takes over thereafter. The following time-line describes what is predicted by the theory.
 
 

• 10^-43 seconds--This is called the Planck Time.
• For shorter times all our current theories break down. Even the very notions of space and time cease to make sense.

• 10^-36 seconds--Temperature about 10²⁸ K.
• This is the era of hyper-expansion called inflation. The maximum distance that light could have traveled since the beginning is a mere

                               3 x 10^-26 centimeters!

This defines the size of the "visible universe" at that time. The universe expands from this microbubble  by a factor of 10 trillion trillion (10²⁵) in about one 1 billion trillion trillionths of a second (10^-33  seconds). This is surely expansion with a vengence! The universe is now about 3 mm across.

The tiny quantum vacuum energy density fluctuations that existed in the original microbubble have also been expanded by this huge factor. They will form the seeds of galaxies.

The remaining vacuum energy is transformed explosively into ordinary matter and energy causing the universe to become extremely hot and to expand at a leisurely pace.
 

• 10^-6 seconds--Temperature about 10 trillion K.
• Quark and anti-quarks form out of pure energy and immediately annihilate back to energy. But, owing to an asymmetry between the behavior of matter and antimatter, an excess of quarks over anti-quarks of one part per billion builds up. Thus, most of the antimatter disappears from our universe.

 
• The quarks stick together to form neutrons and protons. The conversion of protons into neutrons and vice versa maintains an equilibrium with equal numbers of each.

 
• 1 second
• Because neutrons are slightly heavier than protons it is easier to convert neutrons into protons than to convert protons into neutrons and so the number of protons increases relative to neutrons, giving a final proton to neutron ratio of about 7 to 1.

 
• 5 seconds--Temperature about one billion K.
• Electron and positron pairs are created. Matter creation ceases.

 
• 3 minutes--Temperature about 100 million K.
• Nuclear reactions occur at a furious rate. Protons now move slowly enough to fuse into helium nuclei. Helium, deuterium, lithium created.

 
• 300,000 years--Temperature about 10,000 K.
• The radiation density is now low enough that the universe becomes transparent. It is cool enough now for electrons and nuclei to stick together to form atoms of hydrogen and helium. This is called the recombination era.

 
• 1 to 5 billion years--Temperature a few Kelvin.
• The density fluctuations (lumpiness) in the matter distribution, caused by the original quantum fluctuations in the vacuum energy, form the seeds of galaxies, which form in huge web-like sheets spanning the universe. It is these initial density fluctuations that the COBE satellite detected.

 
• 12 billion years--Temperature a few Kelvin.
• Dawn of life on at least one tiny blue planet.

 
• 15 billion years--Temperature 2.7 K.
• More-or-less intelligent life exists on this blue planet!