The gravitino problem in supersymmetric warm inflation

The warm inflation paradigm considers the continuous production of radiation during inflation due to dissipative effects. In its strong dissipation limit, warm inflation gives way to a radiation dominated Universe. High scale inflation then yields a high reheating temperature, which then poses a severe gravitino overproduction problem for the supersymmetric realisations of warm inflation. In this paper we show that in certain class of supersymmetric models the dissipative dynamics of the inflaton is such that the field can avoid its complete decay after inflation. In some cases, the residual energy density stored in the field oscillations may come to dominate over the radiation bath at a later epoch. If the inflaton field finally decays much later than the onset of the matter dominated phase, the entropy produced in its decay may be sufficient to counteract the excess of gravitinos produced during the last stages of warm inflation.