Electron-positron annihilation in cosmology

After neutrino decoupling, electron-positron annihilation transfers entropy to photons but not to neutrinos. Comparing the electromagnetic entropy degrees of freedom before and after annihilation gives $T_{\nu }/T_{\gamma }=(4/11{)}^{1/3}$.

For $T\ll m_e$ and negligible chemical potentials, the combined equilibrium density of electrons and positrons divided by the photon number density isThe exponential suppression eventually makes pair equilibrium incompatible with the residual electrons required by charge neutrality.