How flat is the Universe?

Abstract

In order to answer this question, we combine ten independent astrophysical constraints in the space of the density parameters ${\Omega }_m$ of gravitating matter and ${\Omega }_{\Lambda }$ of vacuum energy. We find that ${\Omega }_m=0.31\pm 0.07$, ${\Omega }_{\Lambda }=0.63\pm 0.21$, and thus ${\Omega }_m+{\Omega }_{\Lambda }=0.94\pm 0.22$. The total ${\chi }^2$ is 4.1 for 8 degrees of freedom, testifying that the various systematic errors included are generous. We also determine ${\Omega }_m$ in the exactly flat case. Five supplementary flat-case constraints can then be included in our fit, with the result ${\Omega }_m=1-{\Omega }_{\Lambda }=0.337\pm 0.031$. It follows that the age of the Universe is $t_0=13.5\pm 1.3$ (0.68/h) Gyr.

11 Pages, 1 Figure, LaTeX2e