Moduli backreaction and supersymmetry breaking in string-inspired
  inflation models
  We emphasize the importance of effects from heavy fields on supergravity
models of inflation. We study, in particular, the backreaction of stabilizer
fields and geometric moduli in the presence of supersymmetry breaking. Many
effects do not decouple even if those fields are much heavier than the inflaton
field. We apply our results to successful models of Starobinsky-like inflation
and natural inflation. In most scenarios producing a plateau potential it
proves difficult to retain the flatness of the potential after backreactions
are taken into account. Some of them are incompatible with non-perturbative
moduli stabilization. In natural inflation there exist a number of models which
are not constrained by backreactions at all. In those cases the correction
terms from heavy fields have the same inflaton-dependence as the uncorrected
potential, so that inflation may be possible even for very large gravitino
masses.
