1998AJ....116...31B

This paper presents a way of finding mutually consistent values of Ω_M_, t₀, and H₀. This approach is illustrated using recent Coma Cluster distance data, together with recent Hipparcos data for RR Lyrae stars. The age of the universe is derived by two completely independent methods, both linked to the RR Lyrae stars. The two methods can be made to yield the same answer by adjustment of the RR Lyrae magnitude zero point. One of these two age determinations is based on stellar evolution in globular clusters, and the other is based on the Hubble constant derived from globular clusters as distance indicators calibrated in the Milky Way. If, for example, RR Lyrae stars are brighter than previously thought, the stellar evolution age is shortened, whereas the Hubble age is increased, so one can determine the RR Lyrae magnitude zero point that would make the stellar evolution age coincide with the Hubble age, and ask whether it is a reasonable value. The answer depends strongly on the mass density of the universe, Ω_M_, which can therefore be derived simply by demanding that the two age determinations agree. For each straw-man value of Ω_M_, we find the RR Lyrae zero point M_V_(RR)0_ for which the two age determinations coincide. We then choose the Ω_M_ value for which the implied RR Lyrae zero point best agrees with observations. In the present paper, the mean of six recent Hipparcos values, M_V_(RR)0_ = 0.61±0.15, is used for illustration. For that choice, the coinciding of ages occurs at 12.5±1.5 Gyr. The corresponding value of the Hubble constant is H₀ = 61±5 km.s^–1.Mpc^–1.

In a zero-Λ universe, the implied mass density is Ω_M_ = 0.41 with only weak constraints on either higher or lower Ω_M_ values. In a flat universe with Ω_M_ + Ω_Λ = 1, however, the implied mass density is Ω_M_ = 0.62, and the uncertainty in it is asymmetric. For example, a critical-density universe with Ω_M_ = 1.0 and Ω_Λ = 0.0 (for which H₀ = 57 km.s^–1.Mpc^–1 and t₀ = 11.4 Gyr) differs by only 0.7 σ, and is therefore not strongly negated, whereas a low-density universe with Ω_M_ = 0.1 and Ω_Λ = 0.9 (for which H₀ = 74 km.s^–1.Mpc^–1 and t₀ = 17.0 Gyr) differs by 3 σ, and therefore appears unlikely.