  The Hubble constant during the last stages of inflation in a broad class of
models based on the KKLT mechanism should be smaller than the gravitino mass, H
<~ m_{3/2}. We point out that in the models with large volume of
compactification the corresponding constraint typically is even stronger, H <~
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.
