Gravitino Production in a Thermal Universe

Abstract

We calculate the abundance of spin 1/2 gravitinos produced in a thermal Universe. On considering that finite thermal energy density of the Universe breaks supersymmetry, we see that the production rate of these gravitino states is enhanced and an excessive abundance of gravitinos of mass 1 keV and 100 GeV is obtained. We derive that the abundance of gravitinos is proportional to reheat temperature of the Universe as $T_\mathrm{reh}^3$, and can be reduced if $T_\mathrm{reh}$ is less than 100 GeV and $4\times 10^4 \mathrm{\,GeV}$ respectively. Such low reheat temperatures will eliminate many models of baryogenesis.