COSMOLOGY, THEORIES

John D. Barrow

The twentieth century has seen cosmology transformed from metaphysics into a branch of physics, and the laws governing fundamental forces and elementary particles have been wedded to astronomical observations to produce a description of the past and present states of the visible universe.

Prior to the creation of the general theory of relativity in 1915 by Albert Einstein, no attempts had been made to produce a mathematical description of the entire universe. Einstein's new relativistic theory of gravitation allowed consistent mathematical models of entire universes - even those with infinite size - to be formulated. Einstein's equations describe how these universes will change in time and from place to place. The simplest possible universe that can arise is one that is unchanging in time and uniform from place to place. This static universe was first proposed by Einstein in 1917 as a manifestation of the centuries-old prejudice that the universe as a whole be unchanging. In order to achieve this static state Einstein had to modify his original equations by the addition of a small constant term (dubbed the ``cosmological constant'') that was allowed, but not required, by the internal consistency of the theory. Subsequently, in the 1920s, it was shown by Willem de Sitter, Alexander Friedmann, and Georges Lemaître that such static solutions are of a very special sort that would not arise in practice; the slightest deviation from perfect uniformity would cause the universe either to expand or contract as a whole. Following this discovery attention focused upon universes that expand in time.

In the late 1920s Edwin Hubble discovered that the light from distant galaxies is shifted in the direction of the red end of the spectrum of visible light by an amount that is directly proportional to their distance away from us. This redshifting of the spectrum is characteristic of the Doppler shift produced by a receding source of radiation. These observations established the expanding-universe theory as the basic paradigm of twentieth-century cosmology.

The standard theory of the expanding universe is a reconstruction of its past history and is usually called the Hot Big Bang theory (a term invented by Fred Hoyle), because the expansion implies that the universe was hotter and denser in the past. The expansion and the attractive

The expansion and the attractive nature of gravity imply that the expansion must have begun at some finite past time (about 15 billion years ago) if the laws of physics and the theory of general relativity apply unchanged at all times in the past. However, it is known that general relativity must cease to be a good description of the universe when it is less than 10^-43 s from its apparent beginning and its density exceeds the Planck value of 10⁹⁶ g cm^-3. To extend the Hot Big Bang theory into these first instants of time we require a quantum theory of gravitation. The search for such a theory, and hence a new quantum cosmology, is at present the greatest unsolved problem in physics. The

The only viable alternative to the Hot Big Bang model that has been suggested is the steady-state theory, proposed in 1948 by Thomas Gold, Hermann Bondi, and Hoyle. This is an expanding universe that remains the same at all times on the average. Whereas the density of matter falls as the Hot Big Bang models expand, and all the matter was apparently created at some finite past time, the steady-state model proposed that there is continuous creation of matter at a rate that exactly counterbalances the natural dilution of the density by the expansion.

In the steady-state theory the universe was predicted to be the same on the average at all times as well as in all places. During the 1950s observational evidence against this theory mounted. Astronomers discovered more astronomical radio sources at large distances than nearby. Since radio waves travel at the speed of light, the distant sources must have emitted their radiation earlier than those nearby. This shows that the average properties of the universe change with the passage of time. In 1965, the discovery of the 3-K microwave background radiation, which is expected as a relic of an earlier hotter and denser phase of cosmic evolution, confirmed the Hot Big Bang theory, and the steady-state theory ceased to be a plausible cosmological model.

The expanding universe exhibits a number of remarkable properties and the explanation of these properties requires detailed extensions of the Hot Big bang theory.

The expansion of the universe is extremely uniform and isotropic over the largest observed dimensions. The temperature of the microwave radiation is the same in every direction to within a few parts in 100,000. Hence the simplest cosmological models, which assume isotropic and uniform expansion, are an excellent approximation to the structure of the real universe. Two particular problems remain for the theory to explain? Why is the universe expanding in such a uniform and isotropic fashion when there would seem to be so many ways for it to be irregular and chaotic? What is the origin of the non-uniformities in the density that now exist in the form of galaxies and clusters of galaxies?

In the early 1970s the favorite theory for the origin of the large-scale uniformity of the universe was the ``chaotic cosmology'' of Charles Misner. It proposed that no matter how the universe began there always arise natural processes that smooth out the irregularities and anisotropies as the expansion proceeds. So long as the expansion lasts long enough, the universe will appear uniform and isotropic to observers like ourselves living about 15 billion years after the expansion began in a chaotic state. Unfortunately, this idea could not explain the observed regularity of the universe regardless of the starting state, and in 1981 the author and Richard A. Matzner showed that any universal smoothing process would produce far more heat radiation than is observed in the universe. All expanding-universe theories regard galaxies as islands of above-average density that began as very small enhancements. During the expansion history of the universe the gravitational force amplifies these overdense regions at the expense of the underdense ones. The question that cosmological theories must answer is this: What is the source and pattern of the original small overdensities that start the process and how intense are they?

Expanding universes need not continue to expand forever. They do so if their average density is below a critical value. But if their average density exceeds this value then at some time in the future the expansion will be reversed into contraction. Redshifted radiation from distant sources will become blueshifted and the universe will collapse toward a ``Big Crunch'' of ever-increasing density and temperature.

One of the most puzzling properties of our universe is that it is now expanding at a rate very close to the critical divide separating the ever-expanding universes from the recollapsing ones. It is a puzzle because as the universe expands it tends to deviate steadily from the critical divide because of the attractive force of gravity. In order that we be as close to the divide as is observed today, the universe must have begun expanding extraordinarily close to the divide originally.

Since 1981 cosmologists have focused attention upon a refinement of the expanding Hot Big Bang theory - called the inflationary-universe theory by its originator, Alan Guth. It proposes that for some finite period of time during the first instants of its expansion the dominant form of matter in the universe exhibited gravitational repulsion rather than attraction. This requires the sum of the matter density plus the pressure stresses exerted in the three directions of space to be negative. (Current theories of elementary particles predict that such forms of matter can arise in the high-density environment expected in the first moments of the universe.) For this period the universe will then accelerate rather than decelerate (as it does at all times in the standard Hot Big Bang theory). The consequences of this acceleration are dramatic. The universe is driven very close to the critical divide, rather than away from it, as in the standard decelerating models. The universe tends to become uniform and isotropic regardless of how it started out and a particular type of seed irregularity is created everywhere in the universe. It remains to be seen whether this form of irregularity can successfully explain the existence of galaxies.

The inflationary-universe theory is the most promising current edition of the Hot Big Bang theory. But it leaves many important questions unanswered. It does not predict on which side of the critical divide we lie - only that we should be close to it. It does not tell us whether the universe is finite or infinite, or whether it had a beginning in time. The answer to these questions must at least await the creation of a quantum theory of the universe as a whole.

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11. See also Cosmology, Big Bang Theory; Cosmology, Inflationary Universe; Gravitational Theories.