2. AGE OF THE UNIVERSE t₀

The strongest lower limits for t₀ come from studies of the stellar populations of globular clusters (GCs). In the mid-1990s the best estimates of the ages of the oldest GCs from main sequence turnoff magnitudes were t_GC 15-16 Gyr (Bolte & Hogan 1995; VandenBerg, Bolte, & Stetson 1996; Chaboyer et al. 1996). A frequently quoted lower limit on the age of GCs was 12 Gyr (Chaboyer et al. 1996), which was then an even more conservative lower limit on t₀ = t_GC + t_GC, where t_GC 0.5 Gyr is the time from the Big Bang until GC formation. The main uncertainty in the GC age estimates came from the uncertain distance to the GCs: a 0.25 magnitude error in the distance modulus translates to a 22% error in the derived cluster age (Chaboyer 1995).

In spring of 1997, analyses of data from the Hipparcos astrometric satellite indicated that the distances to GCs assumed in obtaining the ages just discussed were systematically underestimated (Reid 1997, Gratton et al. 1997). It follows that their stars at the main sequence turnoff are brighter and therefore younger. Stellar evolution calculation improvements also lowered the GC age estimates. In light of the new Hipparcos data, Chaboyer et al. (1998) have done a new Monte Carlo analysis of the effects of varying various uncertain parameters, and obtained t_GC = 11.5 ± 1.3 Gyr (1), with a 95% C.L. lower limit of 9.5 Gyr. The latest detailed analysis (Carretta et al. 1999) gives t_GC = 11.8 ± 2.6 Gyr from main sequence fitting using parallaxes of local subdwarfs, the method used in the 1997 analyses quoted above. These authors get somewhat smaller GC distances when all the available data is used, with a resulting t_GC = 13.2 ± 2.9 Gyr (95% C.L.).

Stellar age estimates are of course based on standard stellar evolution calculations. But the solar neutrino problem reminds us that we are not really sure that we understand how even our nearest star operates; and the sun plays an important role in calibrating stellar evolution, since it is the only star whose age we know independently (from radioactive dating of early solar system material). An important check on stellar ages can come from observations of white dwarfs in globular and open clusters (Richer et al. 1998).

What if the GC age estimates are wrong for some unknown reason? The only other non-cosmological estimates of the age of the universe come from nuclear cosmochronometry - radioactive decay and chemical evolution of the Galaxy - and white dwarf cooling. Cosmochronometry age estimates are sensitive to a number of uncertain issues such as the formation history of the disk and its stars, and possible actinide destruction in stars (Malaney, Mathews, & Dearborn 1989; Mathews & Schramm 1993). However, an independent cosmochronometry age estimate of 15.6 ± 4.6 Gyr has been obtained based on data from two low-metallicity stars, using the measured radioactive depletion of thorium (whose half-life is 14.2 Gyr) compared to stable heavy r-process elements (Cowan et al. 1997, 1999). This method could become very important if it were possible to obtain accurate measurements of r-process element abundances for a number of very low metallicity stars giving consistent age estimates, and especially if the large errors could be reduced.

Independent age estimates come from the cooling of white dwarfs in the neighborhood of the sun. The key observation is that there is a lower limit to the luminosity, and therefore also the temperature, of nearby white dwarfs; although dimmer ones could have been seen, none have been found (cf. however Harris et al. 1999). The only plausible explanation is that the white dwarfs have not had sufficient time to cool to lower temperatures, which initially led to an estimate of 9.3 ± 2 Gyr for the age of the Galactic disk (Winget et al. 1987). Since there was evidence, based on the pre-Hipparcos GC distances, that the stellar disk of our Galaxy is about 2 Gyr younger than the oldest GCs (e.g., Stetson, VandenBerg, & Bolte 1996, Rosenberg et al. 1999), this in turn gave an estimate of the age of the universe of t₀ 11 ± 2 Gyr. Other analyses (cf. Wood 1992, Hernanz et al. 1994) conclude that sensitivity to disk star formation history, and to effects on the white dwarf cooling rates due to C/O separation at crystallization and possible presence of trace elements such as ²²Ne, allow a rather wide range of ages for the disk of about 10 ± 4 Gyr. One determination of the white dwarf luminosity function, using white dwarfs in proper motion binaries, leads to a somewhat lower minimum luminosity and therefore a somewhat higher estimate of the age of the disk of ~ 10.5^+2.5_-1.5 Gyr (Oswalt et al. 1996; cf. Chabrier 1997). More recent observations (Leggett, Ruiz and Bergeron 1998) and analyses (Benvenuto & Althaus 1999) lead to an estimated age of the galactic disk of 8 ± 1.5 Gyr.

We conclude that t₀ 13 Gyr, with ~ 11 Gyr a lower limit. Note that t₀ > 13 Gyr implies that h 0.50 for matter density _m = 1, and that h 0.73 even for _m as small as 0.3 in flat cosmologies (i.e., with _m + = 1). If t₀ is as low as ~ 11 Gyr, that would allow h as high as 0.6 for _m = 1.