Supersymmetric Leptogenesis and the Gravitino Bound

Supersymmetric thermal leptogenesis with a hierarchical right-handed neutrino mass spectrum requires the mass of the lightest right-handed neutrino to be heavier than about 10^9 GeV. This is in conflict with the upper bound on the reheating temperature which is found by imposing that the gravitinos generated during the reheating stage after inflation do not jeopardize successful nucleosynthesis. In this paper we show that a solution to this tension is actually already incorporated in the framework, because of the presence of flat directions in the supersymmetric scalar potential. Massive right-handed neutrinos are efficiently produced non-thermally and the observed baryon asymmetry can be explained even for a reheating temperature respecting the gravitino bound if two conditions are satisfied: the initial value of the flat direction must be close to Planckian values and the phase-dependent terms in the flat direction potential are either vanishing or sufficiently small.