Radiation-dominated universe ($a(t)\propto t^{1/2}$)

A radiation-dominated universe has expansion controlled mainly by radiation in cosmology. When spatial curvature and the cosmological constant are negligible, the Friedmann equation and density scaling $\rho \propto a^{-4}$ give the displayed scale factor, with Hubble parameter $H=1/(2t)$.

Adiabatic expansion conserves entropy in a comoving volume: $s{a}^3$ is constant. With $s=(2{\pi }^2/45)g_{\ast s}{T}^3$, it gives $(a_i/a_0{)}^3=(g_{\ast s,0}/g_{\ast s,i})(T_0/T_i{)}^3$. Changes in entropy degrees of freedom must therefore be retained when transporting an early relic density to today, rather than setting $aT$ constant across all particle thresholds.

// Target: cosmology.bigb