Cosmic neutrino background

The cosmic neutrino background is the relic population of neutrinos that thermally decoupled before electron-positron annihilation. Entropy transfer to photons gives

The effective number of neutrino species parametrizes radiation beyond photons through

If a real relativistic scalar decouples when the other coupled particles have entropy degrees of freedom $g_{\ast s}(T_d)$, thenEarlier decoupling and the subsequent annihilation of more coupled species make the scalar colder and suppress its contribution.