R-invariant new inflation model versus supersymmetric standard model

We revisit the implications of the R-invariant new inflation model to the supersymmetric standard model in light of recent discussion of gravitino production processes by the decay of the inflaton and the supersymmetry breaking field. We show that the models with supergravity mediation do not work well together with the R-invariant new inflation model, where the gravitino abundance produced by the decay of the inflaton and the supersymmetry breaking field significantly exceeds the bounds from cosmological observations without fine-tuning. We also show that the models with gauge mediation can go together with the R-invariant new inflation model, where the dark matter abundance and the baryon asymmetry of the universe are consistently explained without severe fine-tuning