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2.5. The Age of the Universe

Measured independent lower bounds on the Hubble constant and on the age of the oldest globular clusters provide a lower bound on H0t0 (= 1.05ht, where H0 ident 100h km s-1Mpc-1 and t0 ident 10tGyr), and thus an interesting constraint in the Omegam - OmegaLambda plane. The exact expressions are computable in the various regions of parameter space. For example, for OmegaLambda = 0, the relation is (e.g., [15], Eq. 2.79)

Equation 5 (5)

where C+1-1 ident cos-1 and C-1-1 ident cosh-1. A very useful approximation in the presence of a cosmological constant, that is an exact solution for a flat universe, is [1]

Equation 6 (6)

where SOmegaa leq 1-1 ident sinh-1 and SOmegaa > 1-1 ident sin-1. A useful crude approximation near H0t0 ~ 2/3 is

Equation 7 (7)

New Developments: Progress is being made in the HST key project to measure H0 based on Cepheids in Virgo and Fornax.

Pro: The method does not depend on fluctuations, GI, biasing, etc. bullet The current error of ~ 20% in the Hubble constant will hopefully be reduced soon to the level of 10% percent. bullet This method is likely to provide the most stringent upper bound on Omegam and lower bound on OmegaLambda.

Con: The errors in the determination of the age of the universe based on globular clusters are uncertain. The major source of error are the distances to Pop-II stars in the globular clusters, and complex stellar evolution issues.

Current Results: The most likely estimates are of h appeq 0.6 - 0.7 [16] and t appeq 1.5 [17], corresponding to ht appeq 1. They seem to favor a possible deviation from the Einstein deSitter model towards low Omegam or high OmegaLambda or both. However, one only needs to appeal to the current ~ 1sigma lower bounds (say h appeq 0.53 and t appeq 1.2) in order to accommodate the Einstein deSitter model.

Figure 1 displays in the Omegam- OmegaLambda plane the ~ two-sigma constraints from the global measures discussed above. Superposed is the main constraint from cosmic flows (Section 4 below). The joint permitted range for Omegam is thus roughly 0.4 to 1.1. Low Omegam models of Omegam leq 0.3 are significantly ruled out.

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