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 m_{3/2}=O(MeV)-O(GeV). We also propose an explicit model which induces the necessary A-term for the right-handed neutrino.