On the supergravity origin of the minimally supersymmetric standard model inflation

We consider the supergravity origin of the recently proposed minimally supersymmetric standard model (MSSM) inflation, which relies on the existence of a saddle point along a dimension 6 flat direction. We derive the conditions that the Kahler potential has to satisfy for the saddle point to exist irrespective of the hidden sector vacuum expectation values. We show that these conditions are satisfied by a simple class of Kahler potentials, which we find to have a form like those in various string theory compactifications. For these potentials, slow roll MSSM inflation requires no fine-tuning of the soft supersymmetry breaking parameters.