The age of the universe, the Hubble constant and the accelerated expansion

The idea of an accelerating universe comes almost simultaneously with the determination of Hubble’s constant by one of the Hubble Space Telescope Key Projects. The age of the universe dilemma is probably the link between these two issues. The age of the universe is calculated by two different ways. Firstly, a lower limit is given by the age of the presumably oldest objects in the Milky Way, e.g., globular clusters. Their ages are calculated with the aid of stellar evolution models which yield 14 Gyr and 10 % uncertainty. These are fairly confident figures since the basics of stellar evolution are quite solid. Secondly, a cosmological age based on the Standard Cosmology Model derived from the Theory of General Relativity. The three basic models of relativistic cosmology are given by the Friedmann’s solutions of Einstein’s field equations. The models are characterized by a decelerated expansion from a spatial singularity at cosmic time t = 0, and whose magnitude is quantified by the density parameter Ω◦, the present ratio of the mass density in the universe to the so-called critical mass density. The critical Friedmann model has the critical mass density, and therefore, it has Ω◦=1, which implies a spatially flat geometry. The present observed density parameter of the universe is approximately Ω◦ = 0.01, all made of baryonic matter, the usual matter in stars, planets and human beings. But the total mass density parameter — baryonic plus non baryonic, visible and dark — is Ωm ◦ = 0.3, derived from large-scale structure dynamics, Given that the non-critical Friedmann models are highly unstable at time t = 0, meaning that any minute difference from a critical model would result, at time t = t ◦ (now), an immensely large difference from Ω◦ = 1, it is generally accepted that the density parameter is precisely equal to 1. The discrepancy with the observed Ω ◦ is considered as circumstantial evidence of the incompleteness nature of science. Eventually, one should find the reason for the difference. The fiducial cosmological age of the universe is thus naturally given by the age of the critical model. 1 It