Volume modulus inflation and the gravitino mass problem

The Hubble constant during the last stages of inflation in a broad class of models based on the Kachru-Kallosh-Linde-Trivedi mechanism should be smaller than the gravitino mass, H less than or similar to m(3/2). We point out that in the models with large volume of compactification the corresponding constraint typically is even stronger, H less than or similar to m(3/2)(3/2), in Planck units. In order to address this problem, we propose a class of models with large volume of compactification where inflation may occur exponentially far away from the present vacuum state. In these models, the Hubble constant during inflation can be many orders of magnitude greater than the gravitino mass. We introduce a toy model describing this scenario, and discuss its strengths and weaknesses.