Determination of the dynamical parameters of the Universe and its age

Abstract

We determine the density parameters $Ω_m$ of gravitating matter and $Ω_Λ$ of vacuum energy, by making a $χ^2$ fit to nine independent astrophysical constraints. Paying rigorous attention to statistical detail, we find that the present best values are $Ω_m=0.31\pm 0.07, Ω_Λ=0.70\pm 0.13$, where these $1σ$ errors are approximately Gaussian (thus trivially convertible to whatever percentage confidence range desired). The total $χ^2$ is 2.5 for 7 degrees of freedom, testifying that the various systematic errors included are generous. Since $Ω_m + Ω_Λ= 1.01\pm 0.15$, it follows that the Einstein-de Sitter model is very strongly ruled out, that also any low-density model with $Ω_Λ=0$ is ruled out, and that a flat cosmology is not only possible, but clearly preferred. In the flat case we find $Ω_m=0.31\pm 0.04$, from which it follows that the age of the Universe is $t_0 = 13.7^{+1.2}_{-1.1}(0.68/h)$ Gyr.