R-invariant New Inflation Model vs 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 or the supersymmetry breaking field. We show that the models with supergravity mediation do not go well with the R-invariant New Inflation model, where the gravitino abundance produced by the decay of the inflaton or 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 R-invariant New Inflation model, where the dark matter and the baryon asymmetry are consistently explained without severe fine-tuning.