2.1. Why the Universe is Old
The large-scale character of spacetime is well established to be a large, nearly homogeneous, expanding 3-space with a (real or imaginary) radius of curvature vastly larger than any microscopic scale. This fundamental structure, which used to seem to require fine tuning of initial conditions, is now understood as a natural causal consequence of inflation, which automatically creates macroscopic spacetimes, exponentially larger than microscopic scales, from microscopic instabilities.
Our time coordinate in this spacetime, now estimated to be about 12 to 14 Gy, is (as Dicke argued) probably selected by our own needs. The simplest of these is the need for a wide variety of chemical elements. The early universe produced nearly pure hydrogen and helium, but biochemistry uses almost all of the chemically active, reasonably abundant elements in the upper half of the periodic table. The time required to manufacture abundant biological elements and stars with earthlike planets is determined by the formation and evolution times of galaxies and stellar populations, setting a minimum age of billions of years.
Curiously, most observations now suggest that we also appear to be living at an intrinsically special time in the history of the expansion. Data on the Hubble constant, the age of the universe, cosmic structure, matter density, and in particular the supernova Hubble diagrams of Riess et al. (1998) and Perlmutter et al. (1999), and microwave background anisotropy, e.g. Miller et al. (1999), de Bernardis et al. (2000), Hanany et al. (2000), all support a cosmological model with close to a spatially flat geometry, a low matter density, and a significant component of ``dark energy'' such as a cosmological constant (see Fukugita 2000 for a review of the data). These models have an intrinsic expansion rate (/3)-1/2 introduced by the cosmological constant , which happens to be comparable to the current Hubble rate H0. The rough coincidence of this fundamental scale, fixed by the energy density of the physical vacuum = / 8 G, with seemingly unrelated astrophysical timescales determined by stellar evolution, has invited anthropic explanations (Weinberg 1987, 1989, 1997, Vilenkin 1995, Efstathiou 1995, Martel et al 1998, Garriga et al. 2000).
The conjecture is that in a large ensemble of universes (a multiverse), most universes have very large values of the cosmological constant which render them uninhabitable; the value we observe is not the most probable one but is typical of that seen by the largest number of observers in the multiverse as a whole. This argument is tied up with another parameter, the amplitude of the fluctuations which produce galaxies, now usually thought to be determined by the detailed shape of the potential controlling cosmological inflation (e.g. Kolb 1997), which may also be determined by selection (Tegmark and Rees 1998). The anthropic prediction of cosmological parameters in multiverses is still tied up in the murky unresolved debates of quantum cosmology which describe the ensemble (Turok and Hawking 1998, Vilenkin 1998a, Linde 1998).
The value of need not be set anthropically. A similar exotic form of dark energy (``Quintessence''), a dynamical scalar field with properties controlled by an internal potential, could evolve in such a way as to adjust to give it a density comparable to the matter density today (e.g. Zlatev et al. 1999). Or perhaps a ``derivable'' fundamental scale of physics exists, corresponding to a vacuum energy density which happens to be about the same as the current cosmic mean density. The current cosmic mean density ( 0.1 mm)-4 (0.003 eV)4 is derivable from Dicke's argument in terms of fundamental constants; the required coincidence (see equation 6 below) is that (mPlanck / mproton)6 tPlanck2.
One way or another, the intrinsic global cosmological parameters are intimately connected with the large numbers (or ``hierarchy problem'') of fundamental physics; but the nature of the connection is still not clear.