Vacuum energy in cosmic dynamics

Abstract

The analysis of the Th/U ratio in meteorites and the evolutionary ages of globular clusters favour values of the cosmic age of (19±5)×109 yr. This evidence together with a Hubble parameterH 0>70 km s−1 Mpc−1=(14×109 yr)−1 cannot be reconciled in a Friedmann model with Λ=0. It requires a cosmological constant in the order of 10−56 cm−2, equivalent to a vacuum densityρ v =10−29 g cm−3 The Friedmann-Lemaitre models (Λ>0) with a hot big-bang have been calculated. They are based on a present value of the baryonic matter density ofρ 0=0.5×10−30 g cm−3 as derived from the primordial4He and2H abundances. For a Hubble parameter ofH 0=75 km s−1 Mpc−1, our analysis favours a set of models which can be represented by a model with Euclidean metric (density parameter Ω0=1.0, deceleration parameterq 0=−0.93, aget 0=19.7×109 yr) and by a closed model with perpetual expansion (Ω0=1.072,q 0=−1.0, aget 0=21.4×109 yr). A present density parameter close to one can indeed be expected if the conjecture of an exponential inflation of the very early universe is correct. The possible behaviour of the vacuum density is demonstrated with the help of Streeruwitz' formula in the context of the closed model with an inflationary phase at very early times.