The inflatino problem in supergravity inflationary models

We consider the potential problems due to the production of inflatinos and gravitinos after inflation. Inflationary models with a single scale set by the microwave background anisotropies have a low enough reheat temperature to avoid problems with the thermal production of gravitinos. Moreover, the nonthermal production of gravitinos has been shown to be sufficiently small if the sector ultimately responsible for supersymmetry breaking is coupled only gravitationally to the inflationary sector. Still, in some models, inflatinos can be created during preheating with a substantial abundance. The main contribution to the gravitino abundance may thus come from their decay into the inflaton, or into its scalar partner, as well as from the inverse processes. We show that this production needs to be strongly suppressed. This suppression can be realized in the simplest scenarios which typically have a sufficiently high inflationary scale.