Gravitino thermal production revisited and a new cosmological scenario of gauge mediation

We present a new scenario of gravitino dark matter which is compatible with the thermal leptogenesis. We confirm by an explicit calculation in supergravity that the relic abundance of thermally produced gravitino becomes insensitive to the reheating temperature once the temperature of the Universe exceeds the mass scale of the messenger fields. In such a situation, the correct baryon to dark matter ratio can be obtained by thermal leptogenesis when the reheating temperature after inflation is high enough. We demonstrate in a concrete model of gauge mediation that the correct abundance of gravitino and baryon asymmetry can be reproduced by considering the late-time entropy production from the decay of the SUSY-breaking pseudo-moduli field. The scenario is realized when the gravitino mass is 100 MeV lesssim m_{3/2} lesssim 1 GeV, and the messenger mass scale is 10^6 GeV lesssim M_{mess} lesssim 10^9 GeV.