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 the leading 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, and assuming that the other particles are close to thermal equilibrium, the helicity-1/2 gravitino regeneration rate is found to be insensitive to magnetic Debye screening and of order alpha(s)(T) log(1/alpha(s)(T))\m(soft)/F\T-2(3)(1+alpha(s)(T)log(1/alpha(s)(T))+T-2/\f\) up to a calculable, model-dependent O(1) numerical factor. We review the implications of this regeneration rate for supergravity cosmology, focusing in particular on scenarios for baryogenesis.