% miko:type: atomic
% miko:title: Matter-Radiation Equality
% miko:summary: The epoch when matter and radiation energy densities were equal.
% miko:tags: cosmology
% miko:difficulty: undergrad
% miko:related: complete-cosmology, friedmann-equations, cosmic-microwave-background
% miko:keywords: early universe, density scaling, structure formation

\documentclass{article}
\usepackage{amsmath}
\title{Matter-Radiation Equality}
\begin{document}
\maketitle

\section{Density Scaling}

Radiation scales as

$$
\rho_r\propto a^{-4},
$$

while nonrelativistic matter scales as

$$
\rho_m\propto a^{-3}.
$$

\section{Equality}

Matter-radiation equality occurs when $\rho_m=\rho_r$. Before equality,
radiation dominates expansion; after equality, matter dominates until dark
energy becomes important.

\end{document}
