Gravitino production in the warm inflationary scenario

We estimate the production of gravitinos during and after the end of a period of warm inflation, a model in which radiation is produced continuously as the field rolls down the potential producing dissipation. We find that gravitino production is efficient for models in the strong dissipation regime, with the result that standard nucleosynthesis is disrupted unless the magnitude of the inflaton potential is very small. Combining this with the constraint from the thermal production of adiabatic density perturbations we find the dissipation rate must be extraordinarily strong, or that the potential is very flat.