Scalar Decay into Gravitinos in the Presence of D-term SUSY Breaking

Scalar decay into gravitinos is studied in the presence of D-term supersymmetry (SUSY) breaking. The gravitinos produced by the decay of coherent oscillations of scalar fields, such as moduli and inflatons, cause cosmological problems. We show the general formula for the partial decay rate of the scalar into two gravitinos. Applying it to a concrete model of D-term SUSY breaking, we find that D-term SUSY breaking can suppress gravitino production.