Constraints on inflation models from supersymmetry breakings

Effects of soft SUSY-breaking terms on inflation potentials are discussed. There exist generic constraints that must be satisfied in order not for the inflaton potential to loose its flatness. We examine explicitly the constraints in the case of a hybrid inflation model and find that the coupling constant λ between the inflaton and the “water-fall-direction” field is bounded as 2.0×10−6≲λ. This is a highly non-trivial result. Indeed, if we adopt the severest constraint from avoiding the problem of the gravitinos produced non-thermally, λ≲7.4×10−6 is required, under a reasonable assumption on the reheating process. This means that the hybrid inflation model marginally has a viable parameter space. We also discuss analogous constraints on other inflation models.