DOES THE UNIVERSE REALLY EXPAND?

One might be inclined to think, given the popularity of the big bang theory today, that we must by now have solid evidence that the universe is indeed expanding. But in truth, that most fundamental premise to the big bang cosmology remains an assumption. Attempts to show its truth observationally have frustrated astronomers for decades. Moles recently summarized the four classical tests for expansion.⁵ These involve the relationships between the redshift of galaxies on the one hand, and apparent magnitude, surface brightness, number counts, or angular size of galaxies on the other hand. The redshift of galaxy light is assumed to be caused by the velocity of the galaxy away from us. We are here examining tests of the correctness of that assumption. In the next section we will mention some alternative interpretations of redshift for galaxies. To be clear on this point, it is well established that the redshift of ordinary galaxies (although not radio galaxies, Seyfert galaxies, "active galactic nuclei", or quasars) is closely correlated with the distance of those galaxies. But is not well established that the redshift is caused by an increase in that distance.

These classical tests are somewhat complicated with respect to proving or disproving the expansion hypothesis by the influence of unknown evolutionary effects. But these galactic evolutionary effects themselves, and also supernova lightcurves and the ages of globular clusters and galaxy superclusters, each offer the possibility of specialized tests of the expansion hypothesis. We can also easily test non-expanding (static) models, since these generally have no evolutionary effects.

One great difficulty in applying observational tests to galaxy samples is the influence of Malmquist bias. Galaxy sizes do not seem to have any definite maximum, but very large galaxies are rare compared to those of average size. So if we take a small sample of galaxies, it probably will not contain any galaxies very much larger than normal. But the larger our sample becomes, the more extreme the largest galaxy in it is likely to be.

So as we look farther out into the universe, two things happen simultaneously: We start to lose the smaller galaxies from our samples because they are too faint to be seen; and the total number of galaxies increases with roughly the cube of distance. The first fact tends to push the average galaxy in our samples toward the brighter, and therefore larger, galaxies. The second fact implies that the brightest galaxies in our samples will tend to get brighter with distance simply because a larger sample will tend to find more abnormally large galaxies than a smaller sample would. Both effects bias our samples toward larger, brighter galaxies as distance increases. Astronomers must make the effort to compensate for this using appropriate sampling techniques, or the observational test results may become misleading.

For the equations underlying these tests and more details of the analyses, see Moles (1991).⁵