2.2. The Cosmological Tests

Joe Silk and Michael Turner discuss another likely fossil remnant of a time when our universe was very different from now. In the hot Friedmann-Lemaître model helium and other light elements were produced in thermonuclear reactions as the universe expanded and cooled through temperatures kT ~ 1 MeV. This result is the first entry in the second part of Table 1. It uses the Friedmann-Lemaître expression for the expansion rate,

(1)

where

(2)

and a (t) is the expansion factor (such that the distance between conserved objects scales with the expansion of the universe as a (t)). The mass density (t) includes rest mass and the mass equivalent of energy; equation (1) is a relativistic expression. But since you can guess at its form by analogy to Newtonian mechanics it is not a very deep application of general relativity theory. For that we must consider more of the cosmological tests.

The baryon density is an adjustable parameter in this theory. It is impressive that the value of _baryon that yields a satisfactory fit to the the observed abundances of the light element fits the astronomical surveys of the baryon density (Fukugita et al. 1998), but the check is only good to a factor of three or so. The wanted baryon density is less than the mass density parameter _m indicated by dynamical studies of the motions of galaxies relative to the general expansion (as discussed in Section 3.1). That is remedied by an hypothesis, that the mass of the universe is dominated by nonbaryonic matter. The straightforward reading of the dynamical estimates is that _m is less than unity, contrary to the simple Einstein-de Sitter case. A popular remedy is another postulate, that the mass of the universe is dominated by dark matter outside the concentrations of galaxies.

We have a check on _m, from the magnificent work by two groups (Perlmutter et al. 1998a, b; Reiss et al. 1998) on the curvature of the redshift-magnitude (z-m) relation for supernovae of type Ia. A cautionary note is in order, however. The most distant supernovae are fainter than would be expected in the Einstein-de Sitter case. How do we know that is not because the more distant supernovae are less luminous? The authors present careful checks, but the case has to be indirect: no one is going to examine any of these supernovae up close, let alone make the trip back in time to compare distant supernovae to nearer examples. In short, the supernovae measurement is a great advance, beautifully and carefully done, but it does not come with a guarantee. The point is obvious to astronomers but not always to their colleagues in physics, and so might well be encoded in the Tantalus Principle: in astronomy you can look but never touch (with a few exceptions, such as objects in the Solar System, that are quite irrelevant for our purpose).

The straightforward reading of the SNeIa z-m relation within the Friedmann-Lemaître model is that _m is well below unity, consistent with dynamics, and that there is a significant contribution to the stress-energy tensor from Einstein's cosmological constant (or a term in the stress-energy tensor that acts like ). The latter has to be counted as another hypothesis, of course. This in turn can be checked by still more cosmological tests, such as the expansion time. But as discussed in the next section we don't yet have the wanted precision.

Our tour of the second set of tests in Table 1, that probe space-time geometry, shows no postulates that appear artificial, which is encouraging. But we do see that each constraint is met with a new free parameter, which is a dangerous operation, to quote de Sitter (1931).