Precision cosmology made more precise

TL;DR

This paper derives an exact analytic solution to the Friedmann equations with radiation, matter, and cosmological constant in flat space, and quantifies the error of the traditional piecewise approximation.

Contribution

It provides the first exact analytic solution to the combined Friedmann equations and assesses the accuracy of the common piecewise approach.

Findings

Exact solution for Friedmann equations with all components

Quantification of errors in piecewise solutions

Potential for more precise cosmological modeling

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 $R_{\rm pw} (t)$. We instead find the exact and analytic solution $R (t)$ of the same equations in flat space. Moreover, we quantify the error made when $R_{\rm pw} (t)$ is used in place of $R (t)$.