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Moduli rolling to a natural MSSM with gravitino dark matter

We propose the gravitino dark matter in the gravity mediated supersymmetry breaking scenario. The mass hierarchies between the gravitino and other superparticles can be achieved by the nontrivial Kähler metric of the supersymmetry breaking field. As a concrete model, we consider the five-dimensional supergravity model in which moduli are stabilized, and then one of the moduli induces the slow-roll inflation. It is found that the relic abundance of the gravitino and the Higgs boson mass reside in the allowed range without a severe fine-tuning.