Particle production and gravitino abundance after inflation

Thermal history after inflation is studied in a chaotic inflation model with supersymmetric couplings of the inflaton to matter fields. The time evolution equation is solved in a formalism that incorporates both the back reaction of particle production and the cosmological expansion. The effect of the parametric resonance gives rise to a rapid initial phase of the inflaton decay followed by a slow second stage of the decay whose rate is given by the Born approximation. Thermalization takes place immediately after the first explosive stage for a medium strength of the coupling among created particles. As an application we calculate the time evolution of the gravitino abundance that is produced by ordinary particles directly created from the inflaton decay, which typically results in a much more enhanced yield than what a naive estimate based on the Born approximation would suggest.