Gravitino production in a thermal Universe revisited

We study the production of spin 1/2 gravitinos in a thermal Universe. Taking into account supersymmetry breaking due to the finite thermal energy density of the Universe, there is a large enhancement in the cross section of production of these gravitino states. We consider gravitinos with zero temperature masses of 0.1 eV, 1 keV, 100 GeV and 30 TeV as representative of gauge mediated, gravity mediated and anomaly mediated supersymmetry breaking scenarios. We find that the abundance of gravitinos produced in the early Universe is very high for gravitinos of mass 1 keV and 100 GeV. The gravitino abundances can be sufficiently suppressed if the reheat temperature is less than 100 GeV and $4\times10^4 \gev$ respectively. However such low reheat temperatures will rule out many models of baryogenesis including those via leptogenesis.