Precision cosmology made more precise

Abstract

So far, the standard attitude to solve the Friedmann equations in the simultaneous presence of radiation $R$, matter $M$ and cosmological constant $\Lambda$ is to find solutions $R_R(t)$, $R_M(t)$ and $R_{\Lambda }(t)$ separately for each individual component alone, and next to join them together, thereby obtaining a piecewise solution $R_{\mathrm{pw}}(t)$. We instead find the exact and analytic solution $R(t)$ of the same equations in flat space. Moreover, we quantify the error made when $R_{\mathrm{pw}}(t)$ is used in place of $R(t)$.

9 pages, 3 figures