Determination of the dynamical parameters of the Universe and its age

Abstract

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

17 Pages, 1 Figure, LaTeX2e