F - term inflation in Superstring Theories

A supersymmetric inflationary stage dominated by an F-term has the problem that the flatness of the potential is spoiled by supergravity corrections, that is the slow-roll parameter η gets contributions of order unity. We show that in F-term inflationary models based on strings there is natural way of obtaining small values of η. This happens in models of hybrid inflation based on orbifold constructions, in which a modulus T field is responsible for the large value of the potential during inflation, and a second field φ with appropriate modular weight is responsible for the roll-over. We illustrate the mechanism with a model in which the inflaton potential is provided by gaugino condensation, leading to succesful inflation.