On the Thermal Regeneration Rate for Light Gravitinos in the Early Universe

We investigate the light gravitino regeneration rate in the early Universe in models based on $N=1$ supergravity. Motivated by a recent claim by Fischler, we evaluate finite-temperature effects on the gravitino regeneration rate due to the hot primordial plasma for a wide range of the supersymmetry-breaking scale $F$. We find that thermal corrections to the gravitino pole mass and to the Goldstino coupling are negligible for a wide range of temperatures, thereby justifying the extension of the equivalence theorem for the helicity-1/2 gravitino and Goldstino to a hot primordial plasma background. Utilizing the Braaten-Pisarski resummation method, the helicity-1/2 gravitino regeneration rate is found to be $0.25 \alpha_s(T) \log(1/\alpha_s(T))|{m_{\rm soft}/F}|^2 T^3(1 + \alpha_s(T) \log(1/\alpha_s(T)) + T^2 / |F|)$ up to a calculable, model-dependent ${\cal O}(1)$ numerical factor. We review the implications of this regeneration rate for supergravity cosmology, focusing in particular on scenaria for baryogenesis.