Abstract
We show that in generic supergravity theories the mass of the moduli during inflation is larger (or at least of the same order of magnitude) than the Hubble constant. This fact does not depends on the details of the inflation and on the value of the Hubble parameter during it. The reason is that inflationary universe is dominated by large F-term (or D-term) density which is higher than the SUSY breaking scale in the present minimum and stabilizes the flat directions of the supersymmetric vacua. Therefore, in general even standard inflationary scenarios (with large H) may solve the cosmological moduli problem.
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