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 $Ω_m$ of gravitating matter and $Ω_Λ$ of vacuum energy. We find that $Ω_m=0.31\pm 0.07$, $Ω_Λ=0.63\pm 0.21$, and thus $Ω_m + Ω_Λ=0.94\pm 0.22$. The total $χ^2$ is 4.1 for 8 degrees of freedom, testifying that the various systematic errors included are generous. We also determine $Ω_m$ in the exactly flat case. Five supplementary flat-case constraints can then be included in our fit, with the result $Ω_m=1-Ω_Λ= 0.337\pm0.031$. It follows that the age of the Universe is $t_0 = 13.5\pm 1.3$ (0.68/h) Gyr.