Matter-Radiation Equality

Density Scaling

Radiation scales as

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

while nonrelativistic matter scales as

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

Equality

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