Annu. Rev. Astron. Astrophys. 1993. 31: 689-716 Copyright © 1993 by Annual Reviews. All rights reserved

3.6. Parameters

Now that the overall normalization of the CDM input power spectrum has been measured, we return to the classic issues of the global parameters (H₀, ₀). Can one consistently fit observations with the model requirements? In a flat universe without a cosmological constant, the age is t = 2 / (3H₀), so a small Hubble constant is needed in order to avoid an age for the universe that is less than that of constituent parts such as globular dusters. In addition, the need for relatively more large-scale power pushes CDM in the direction of a small value of H₀. As a result of these constraints, those constructing global CDM models have typically adopted H₀ = 50 as the largest possible value consistent with their requirements, and H₀ = 30 would be greatly preferable with regard to large-scale structure questions. The observational situation is, as ever, unresolved. At present, most of the modem indicators seem to produce values of H₀ which cluster in the 70-90 km s^-1/Mpc range (van den Bergh 1989, Tonry 1991), and H₀ = 50 is at least one sigma below current best estimates. Thus, at about the 1.5 level (or worse), one can say that the observed value of H₀ is inconsistent with the needs of standard CDM.

Most estimates of are also below the CDM requirement of unity, but the long observed tendency for dynamical mass estimates to grow with time and to increase with the scale of measurement leaves the issue in substantial doubt. Clusters of galaxies, which should efficiently collect dark matter due to the depth of their potential wells, typically indicate (M/L) 250-300. Then, utilizing the observed light density of the universe, one finds = (M / L) / 1400 0.2. A similar, independent result is obtained from clusters by another route. The ratio of baryonic-to-total mass in the clusters is in the range (for h = 1) 10% to 15% with most of that in X-ray emitting gas. But, from light element nucleosynthesis, the baryonic density is _b = 0.013 h^-2. Then, dividing by the ratio of baryonic-to-total mass from clusters gives an _tot << 1, a point made by White (1992) and others.

There is currently one group of studies that does indicate a relatively large value of from direct dynamical measurements. Dekel et al (1993) (see also Dekel 1991 and Yahil 1990) have combined the IRAS 2Jy survey with redshifts from 10^3.4 galaxies and reasonable assumptions about the velocity field to measure the dynamical mass density on approximately the 50 h^-1 Mpc scale. They find that = 1.4 × 10^±0.3b^5/3, where b, the bias of IRAS galaxy fluctuations over the mass fluctuations on a scale of 12 h^-1 Mpc, may be slightly in excess of unity. While the 95% confidence limits quoted above seem most consonant with a flat model, the result is still of course consistent with open models and, in any case, replication by other workers in other volumes of space is necessary.

Thus, the evidence on the crucial question of the actual value of is mixed. Almost all methods indicate 0.2-0.3 as a best fit, but one careful study is consistent with closure, = 1.