Sharp-freeze-out relic dilution
= Sharp-freeze-out relic dilution
{title2=$n_0=n_f(a_f/a_0)^3$}
In a stable-particle approximation with negligible later <annihilation>, comoving particle number is conserved and physical <number density> falls as $a^{-3}$. Replacing scale-factor ratios by photon-temperature ratios additionally assumes no change in the <entropy degrees of freedom>.