Historical Perspective
Cosmological Facts
Cosmological Concepts
Inflationary Cosmology
1823--Heinrich Olber (German) noted a paradox, which has come to be known as Olber's paradox:In an infinitely large and infinitely old universe the sky would be as bright as the surface of the Sun; so why is the night sky dark?
He reasoned as follows: In an infinite universe of infinite age there would be infinitely many stars. Therefore, if you point to any direction in the sky, eventually your line of sight would intercept a star's surface. Since every direction leads to a star, the sky would appear to be tightly packed with stars. Therefore, the sky would be as bright as the surface of a star.
1848--Edgar Allan Poe (of scary story fame) suggested a way out of this impasse: the universe may be infinitely large but be 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, however, a dynamic universe was thought to be such a crazy idea that even Einstein could not believe the prediction of his own theory.
Therefore, Einstein, modified his theory to make it predict a static universe, that is, a universe that neither expanded nor contracted. 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 space and time near the Sun. The day after Eddington made public his confirmation of Einstein's prediction, Einstein became the most famous scientist in history.
1922--The Russian mathematician Aleksandr Friedmann abandoned Einstein's static universe model and worked out the mathematics and geometry of dynamic (that is, changing) universes. To make progress with the mathematics he made the following simplifying assumption:
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 class of mathematical models that described expanding universes. The calculations were later repeated by the American Howard Robertson in 1935.1924--Edwin Hubble, using work by Henrietta Leavitt on Cepheid variables, measured the distance to 9 galaxies and proved that they are very distant.
1927--Abbe Georges Lemaitre (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.
Lemaitre derived a relationship between (what later turned out to be) Hubble's constant, H, 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)/lewhere lo is the wavelength of the light that reaches Earth and le is the wavelength of the light emitted 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 an example of the Doppler effect.Hubble proposed that the observed red shifts was evidence that the galaxies are receding from us, that is, evidence that the universe is expanding, just as Einstein's original equations predicted.
Einstein's (self-confessed) blunder was his earlier failure to accept this startling prediction. Had he been sufficiently bold he could have made one of the most extraordinary predictions of 20th century science: that the universe is expanding and came into being a finite time ago.
The velocity at which galaxies recede from us is called the recession velocity. Since the galaxies are receding from us, one might be tempted to draw the conclusion that the Earth is at the center of the expanding universe. However, according to the cosmological principle, no place in the universe is privileged; in particular, we do not occupy a privileged position; we are not at the center of the universe. If we moved to another part of the universe we should expect to see more or less the same thing: the galaxies would appear to recede from us.
Here is a recent graph of the red shift-distance relationship which is obtained by studying Type Ia supernovae. See also, the Supernova Cosmology Project home page.
1940s--George Gamow (a Russian and ex-student of Friedmann) and later Ralph Alpher and Robert Herman of Johns Hopkins University refined Lemaitre'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 that would manifest itself as photons of very short wavelengths. The temperature of these primordial photons would be billions of degrees.
But as the universe expands all length scales are stretched by the expansion including the wavelengths of the primordial photons. Recall, that the longer the wavelength the lower a photon's energy. Therefore, as the universe aged, and expanded, 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. This radiation would be literally the afterglow of the earlier extremely hot dense phase of the universe. Alas, for Alpher and Herman, 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. It finally dawned on them that this was not mere noise. In fact, they had discovered, by accident, photon radiation coming from outer space, that was not associated with any known astronomical objects. This radiation, which is in the microwave part of the electromagnetic spectrum, 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 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 discovery of the microwave background! Such is life.
Hubble's LawFor a galaxy a distance d away from us and receding at a speed v it is observed that
where H 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.v = H dAbundances
The matter in the universe consists largely of hygrogen, helium, deuterium and lithium. The observed proportions of these elements in the universe is
Element Nuclear 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 (CMB) Radiation
The CMB 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 BangThe 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
Before we can talk sensibly about the age of the universe we need to agree on what we mean by this phrase.
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. As we shall see shortly, modern estimates are somewhat earlier than this!
We shall define the age of the universe as the time since its creation at the big bang. Let's try to estimate that time period. Consider a galaxy that is a distance d from us and assume (to keep the mathematics simple) that over the age of the universe t the galaxy's recession speed v was constant.
At the big bang, the energy that would eventually become the galaxy was next to the energy that eventually led to us. The age of the universe would be the time it has taken the "galaxy" to move from our immediate vicinity to its current position. Since we know the galaxy's speed, and we assume it has remained constant since the beginning, we can estimate this time as follows
or, when we use Hubble's Law v = Hd ,t = d/vThat is, an approximate value for 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 acts like a break which decelerates the universal expansion. This calculation was first performed by Lemaitre, who obtained:t = 1/Has the age of the universe.t = (2/3) x (1/H)Thequantity 1/H is called the Hubble Time, which according to Lemaitre's calculation is greater than the age of the universe.
Why is this so? Well, if the expansion has been decelerating since the big bang, because of the breaking effect of gravity, then recession speeds must have been greater in the past; that is, galaxies must have receded faster, on average, than they do at present. Consequently, every galaxy must have arrived at its present location, relative to us, sooner than the Hubble time, which is the age we inferred by assuming the recession speed never changed.
If we take Hubble's Constant to be 50 km/sec per megaparsec we predict an age of about 15 billion years, a time it should be note considerably longer than that estimated by Bishop Ussher.
Critical Density and Spacetime
Today we prefer to think of space and time as a single entity called spacetime. The latter is made of 3 space plus 1 time dimension--that is, it is a 4-dimensional volume! Moreover, according to Einstein, 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. General relativity predicts that the 4-dimensional volume can curve in different ways depending upon the density of matter and energy in the universe. In the simplest models of the universe, there are three possible ways in which space can bend:
Open Universe--In this case the global geometry of space has negative curvature. Unfortunately, this is quite impossible to imagine. Negative curvature arises if the matter and 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.Cosmic Horizon--How far can we see?
Closed Universe--In this case the global geometry of space 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 contract and finally collapse in a titanic implosion called (inevitably) the Big Crunch.
Flat Universe--The global geometry of space 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 reach a zero expansion speed in the infinite future. Most cosmologists believe the global geometry of the universe is flat.
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 at present. 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.
Here is a thought to ponder: Presumably mankind, as a species, is not immortal. Therefore, it is quite likely that our species will not survive long enough to see the entire universe. There may well be a limit to what we can know about the universe.
SuccessesThe Inflationary TheoryThe big bang theory is able to account for the following facts:
Universal expansionProblemsMicrowave background radiation
Abundance of light elements
It fails to account for:
Why the microwave background is so uniform (Horizon Problem).Why the galaxies are distributed in vast sheets, surrounding voids (Structure Formation Problem).
Why spacetime is so incredibly flat (Flatness Problem).
Why there are no monopoles and other strange objects in our universe (Monopole Problem).
How something can be created, apparently, from nothing (Creation Problem).
This theory is a modification of the standard big bang model. One postulates the existence of a vacuum endowed with a mysterious form of energy. It is mysterious in that the vacuum, while filled with this energy, still looks empty because it would be devoid of ordinary matter and energy.In the beginning, one assumes the density of this strange vacuum energy to be huge. According to general relativity, the greater the energy density the faster the expansion. Indeed, according to the inflationary theory the energy density was so huge that it caused the universe to expand at a staggering 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.Inflation causes the universe to be stretched by an absolutely enormous factor, so much in fact that any relatively small region of the universe, for example the small region that becomes the entire visible universe, would appear flat, just as a small patch of the Earth's curved surface appears flat even though globally the Earth's surface is curved. 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 and was able to reach a state of uniformity. 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 rapidly decreased. 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.
Timeline
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 mere10-6 seconds--Temperature about 10 trillion K.3 x 10-26 centimeters!
This defines the size of the "visible universe" at that time. The universe expands from this bubble by a factor of 10 trillion trillion (1025) in about one 1 billion trillion trillionths of a second (10-33 seconds). The universe is now about 3 mm across.
Any energy density fluctuations (lumpiness) that existed in the original bubble 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.
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 through annihilation with matter, leaving an excess of matter.1 secondThe 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.
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 to radiation. 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 evolves on this blue planet!
