Late-time entropy production from scalar decay and the relic neutrino temperature

Abstract

Entropy production from scalar decay in the era of low temperatures after neutrino decoupling will change the ratio of the relic neutrino temperature to the CMB temperature, and, hence, the value of ${N}_{\mathrm{eff}},$ the effective number of neutrino species. Such scalar decay is relevant to reheating after thermal inflation, proposed to dilute massive particles, like the moduli and the gravitino, featuring in supersymmetric and string theories. The effect of such entropy production on the relic neutrino temperature ratio is calculated in a semianalytic manner, and a recent lower bound on this ratio, obtained from the WMAP satellite and 2dF galaxy data, is used to set a lower bound of $\ensuremath{\sim}1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}$ GeV on the scalar decay constant, corresponding to a reheating temperature of about $3.3$ MeV.