Soft leptogenesis and gravitino dark matter in gauge mediation

We study soft leptogenesis in gauge mediated supersymmetry breaking models with an enhanced A-term for the right-handed neutrino. We find that this scenario can explain the baryon asymmetry of the present universe, consistently with the gravitino dark matter for a wide range of gravitino mass m3/2=O(MeV)-O(GeV). We also propose an explicit model which induces the necessary A-term for the right-handed neutrino.