4. COMPARISON WITH PREVIOUS WORK

The goal of this paper is to determine the absolute age of the universe t₀(h, _m, ). Knowledge of h alone cannot be used to determine t₀ with much accuracy. For example, the estimate h = 0.68 ± 0.10 corresponds to 8 < t₀ < 22 Ga (Fig. 4). Similary, knowledge of (_m, ) yields H₀t₀ (_m, ) not t₀(H₀ is the usual Hubble constant). When one inserts a preferred value of h into a H₀t₀ result, one is not taking into consideration the correlations between preferred h values and preferred (_m,) values that are inherent, for example, in _CMB(h, _m,) and _baryons(h, _m). The preferred values of h in these likelihoods depend on _m and . Perlmutter et al. (4) used SNe measurements to constrain (_m, ) and obtained values for H₀t₀. To obtain t₀, they did the analysis with h set equal to the value preferred by their SNe data, h = 0.63. Their result is t₀ = 14.5 ± 1.0 (0.63 / h) Ga. When a flat universe is assumed, they obtain t₀^flat = 14.9^+1.4_-1.1 (0.63 / h) Ga. Riess et al. (5) found h = 0.65 ± 0.02 from their SNe data. Marginalizing over this Hubble value and over and _m, they report t₀ = 14.2 ± 1.7 Ga. When a flat universe is assumed, their results yield t₀^flat = 15.2 ± 1.7 Ga. The Perlmutter et al. (4) and Riess (5) results are in good agreement. When I assume h = 0.64 ± 0.02, I get t₀ = 14.6^+1.6_-1.1 Ga. This result is plotted in Fig. 2 to illustrate the important influence on the result of using a small h uncertainty. Efstathiou et al. (12), on the basis of a combination of CMB and Perlmutter et al. (4) SNe data, have estimated t₀ = 14.6 (h / 0.65)^-1 Ga. I used h = 0.65 ± 0.0 with this data combination to get t₀ = 14.5^+1.2_-1.0 Ga. However, when I used h = 0.65 ± 0.10, the result is 0.7 Gy lower (t₀ = 13.8^+3.2_-1.4 Ga). To obtain the main result, I used uncertainties large enough to reflect our knowledge of h on the basis of many sources. The use of a larger h uncertainty contributes to the substantially younger ages found here (23).

A potential problem with the SNe ages is the high region, (_m,) (0.8, 1.5), which dominates the SNe fit. This region is strongly disfavored by the six other constraints considered here (see Fig. 3). These high (_m, ) values allow lower ages than the t₀^flat SNe results because the slope of the iso-t₀ contours (Fig. 3B) is larger than the slope of the SNe contours. The t₀^flat results are not as subject to this problem and are the results most analogous to the result reported here, despite the fact that the SNe t₀^flat results are less consistent with the result reported here. There are several independent cosmological measurements which have not been included in this analysis either because a consensus has not yet been reached [gravitational lensing limits (27, 28, 29, 30)] or because the analysis of the measurements has not been done in a way that is sufficiently free of conditioning on certain parameters [local velocity field limits (31)]. Doubts about some of the observations used here are discussed in (32). There has been speculation recently that the evidence for is really evidence for some form of stranger dark energy that we have incorrectly been interpreting as . Several workers have tested this idea. The evidence so far indicates that the cosmological constant interpretation fits the data as well as or better than an explanation based on more mysterious dark energy (4, 33, 34).