Non-thermal Gravitino Dark Matter in Gauge Mediation

We show that gravitinos produced by decays of a supersymmetry breaking scalar field (the pseudo-moduli field) can naturally explain the observed abundance of dark matter in a certain class of the gauge mediation models. We study the decay processes as well as cosmological constraints on this scenario in detail, particularly focusing on different behavior of the real and imaginary components of the pseudo-moduli field. Cosmologically viable scenario emerges when the gravitino and the pseudo-moduli masses are O(10-100) MeV and O(100) GeV, respectively.