Radiation in cosmology

Cosmological radiation has equation of state $P_r={\rho }_r/3$ and density scaling ${\rho }_r\propto a^{-4}$.

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

For relativistic species in thermal equilibrium at a common temperature $T$, the total energy density can be writtenThe factor $7/8$ is the fermion-to-boson thermal integral ratio for energy density.

For relativistic species at a common temperature, the mass-equivalent energy density is $\rho ={\pi }^2{g}_{\ast }(k_{B}T{)}^4/(30{\hslash }^3{c}^5)$. Using mass rather than energy density accounts for the powers of $c$ in the Friedmann equation.