INTRODUCTION

For most of the existence of our species on this planet, mankind has believed that our home, the Earth, was located at the center of the universe. Copernicus's theory and the Scientific Method finally displaced this strongly held geocentric view with the humbler but more realistic perspective that we are no place special in the universe.

Because this basic perspective change was so difficult to achieve, modern science has since always insisted that any theory seeming to put humans in a special place in the universe was thereby automatically suspect. So when modern cosmologies were first formulated, they were required to obey the "cosmological principle", that the universe should have a uniform matter distribution on the largest scales ("homogeneity"), and look essentially the same for all observers viewing in all directions ("isotropy").

With this background, it therefore came as a surprise in the 1920s when Edwin Hubble found that the light from galaxies appeared redshifted; and that the fainter (and therefore farther away, on average) a galaxy was, the more its light was redshifted. Here was an observable property of the universe that seemed centered on us, and changed uniformly with distance away from us, as if we were at the center of the universe.

The timing of this discovery was critical to further evolution of the theories. At just that time, Einstein's general theory of relativity had received observational support and was gaining in favor with physicists. But there was a serious problem in incorporating general relativity into cosmology. It appeared that gravity made the universe unstable, inducing it to collapse. Wherever galaxies or large assemblies of matter existed, other distant galaxies or assemblies would be attracted toward them; and these mutual attractions would cause all galaxies or large assemblies to be pulled toward one another, since they had insufficient velocity to resist the attraction. Simply put, all sufficiently large structures, including the universe as a whole, must collapse under the weight of mutual gravitation. Yet observations showed this did not happen.

To get around this difficulty, Einstein invented the "cosmological constant" -- a hypothetical repulsive force operating on large scales that prevented the collapse of the universe. This was the unsatisfactory state of affairs when Hubble made his redshift discovery. Physicists of the day immediately knew that, if the redshift of galaxy light was caused by galaxies moving away from us, the implied expansion of the universe would serve to solve the "problem" with the stability of the universe in a far more elegant way.

Friedmann described three possible models in which the universe would appear homogeneous and isotropic, yet be seen as expanding, by all observers in it at the present time:

(1) The open universe, in which the rate of expansion everywhere exceeds the velocity of escape from the rest of the matter in the universe. Such an expansion would continue forever; and space in such a universe can be described as negatively curved.

(2) The closed universe, in which the expansion is eventually halted by gravity and becomes a collapse back to the origin. Such a universe has a finite lifetime unless it bounces and continues expanding and recollapsing forever. Space in this type of universe has positive curvature. As on a sphere, a straight line in any direction eventually returns to its starting point.

(3) The flat universe, in which the expansion is critically balanced at the threshold between open and closed. The expansion goes on forever, asymptotically approaching zero velocity after infinite time has elapsed and the universe has become infinitely large. Space therein has no curvature.

In principle, observations should allow us to determine which type of Friedmann expanding universe we inhabit. We simply measure the cosmic deceleration parameter, q. In a flat universe, the total matter in the universe is just enough to halt the expansion after an infinite time. This corresponds to a cosmic deceleration q0 = 0.5. If the observed value of q0 is larger than 0.5, the universe is closed. If q0 is less than 0.5, the universe is open. If there were no cosmic deceleration, q0 = 0; or if the expansion accelerates due to some hypothetical force of repulsion, q0 < 0. The most widely accepted form of the big bang theory predicts that q0 = 0.5.

Thus, the big bang theory was born from the adoption of Friedmann's premises as the explanation for Einstein's quandary about the collapse of galaxies and Hubble's redshift data. However, in their eagerness to solve these dilemmas, astronomers and physicists were induced to accept a new, if less distressing, way of accepting that the observer was special. It is true that the Earth would occupy no special place in a Friedmann-type universe, and everything would look basically the same in all directions as seen by anyone anywhere. However, everything in the universe would always be at a special time, a finite number of years from the beginning or end of the universe, and evolving accordingly. The universe looked rather different at any two widely spaced moments of time. The Friedmann models still obeyed the original cosmological principle; but they violated the new "perfect" cosmological principle, in which the universe should look essentially the same to any observer at any time as well.

This development was ironic, because one of the accomplishments of the theory of relativity was to show the large extent to which space and time were similar and interchangeable. That symmetry had to be abandoned by the big bang when the perfect cosmological principle was abandoned. As we will discuss, this pragmatic decision to once again allow the observer to be special (observing at a special time) was probably a wrong turn for science.