3.7. Pure Thought
There are three issues to consider: coincidences, inflation, and our taste as to how the world might best end.
If m ~ 0.25 we flourish at a special epoch, just as the universe is making the transition from matter-dominated to - or curvature-dominated expansion within the Friedmann-Lemaître model. Maybe this is pure chance. Maybe it is an effect of selection: perhaps galaxies as homes for observers would not have existed if m were very different from unity (Martel et al. 1998 and references therein). Maybe there is no coincidence: perhaps m really is close to unity. Most of us consider the last the most reasonable possibility. But the observational entries in Table 2 show that if m = 1 then Nature has presented us with a considerable set of consistently misleading clues. The much more likely reading of the evidence is that, within the Friedmann-Lemaître model, m 0.25. We should pay attention to arguments from aesthetics; the history of physical science has many examples of the success of ideas driven by logic and elegance. But there are lots of examples of surprises, too. The evidence that m is significantly less than unity is a surprise. I enter it as a demerit for the Friedmann-Lemaître model, but not a serious one: surprises happen.
The conventional inflation picture accounts for the near homogeneity of the observable universe by the postulate that an epoch of near exponential expansion driven by a large effective cosmological constant stretched all length scales in the primeval chaos to unobservably large values, making the universe we can see close to uniform. The same process would have made the radius of curvature of space very large. Thus in their book, The Early Universe, Kolb & Turner (1988) emphasize that a sensible inflation theory requires negligibly small space curvature: m may be less than unity, but if it is a cosmological constant makes m + equal to unity. The argument is sensible but model-dependent. Gott (1982) pioneered a variant of inflation that produces a near homogeneous Friedmann-Lemaître model with open space sections. Ratra & Peebles (1994) revived the concept; details of the history and application are in Górski et al. (1998). Most proponents of inflation I have talked to share the preference for m + = 1 but agree that they could learn to live with the open version if that is what the observations required. The flat low density case does get the higher grades in Table 2, from the z-m relation and the CBR anisotropy, but my impression is that both results are too preliminary to support a decision on open versus flat space sections.
The values of the cosmological parameters tell us how the world ends
according to the Friedmann-Lemaître model, whether it is collapse
back to a Big Crunch or expansion into the
indefinitely remote future. But why should we pay attention to
an extrapolation into the remote future of a theory
we can be pretty sure is at best only an approximation to reality? For
example, suppose improved tests showed that
m = 0.2, that the
of Einstein's cosmological constant is quite small,
|| << 1, and that space
curvature correspondingly is negative. The straightforward
interpretation would be that our universe is going to expand
forever more, but it need not follow. If were
constant and less than zero, then no matter how small
Friedmann-Lemaître model would predict
that the expansion will
eventually stop and the universe will contract back to a Big
small negative value. This may be of some comfort if the Big Crunch is
more to your taste. To my taste the main lesson is that we should stop
all this talk about how the world ends until we can think of some
scientific meaning to attach to the answer.
2 The example is contrived but not entirely frivolous. Standard and successful particle theory includes a cosmological constant, in the form of the energy density of the vacuum, but quite fails to explain why its value is in the observationally acceptable range. Until we have a deeper theory that deals with this I don't see how we can exclude the idea that it has or ends up with an exceedingly small negative value. Back.