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

Abstract

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 $0.25{\alpha }_s(T)\log (1/{\alpha }_s(T))|m_{\mathrm{soft}}/F{|}^2{T}^3(1+{\alpha }_s(T)\log (1/{\alpha }_s(T))+T^2/|F|)$ up to a calculable, model-dependent $\mathcal{O}(1)$ numerical factor. We review the implications of this regeneration rate for supergravity cosmology, focusing in particular on scenaria for baryogenesis.

Comments: REVTEX 32 pages, two encapsulated ps figure files