On the fate of coupled flat directions during inflation
  We investigate the stochastic dynamics of the long wavelength modes of a
generic light scalar field that during inflation is coupled to another scalar
field. The coupling plays an important role for the fluctuation of the field
amplitude and may block its initial growth. We find that such a blocking is
avoided, albeit only temporarily, if the light scalar has an initial
non-vanishing expectation value <\phi> larger than a certain critical value,
for which we provide an estimate. We also show that the field fluctuations will
eventually reach an equilibrium amplitude provided inflation is sufficiently
long-lasting. We present a novel, general expression for the variance <\phi^2>
that takes into account the coupling of the massless field and describes the
growth during the epoch of quasi-free fluctuations as well as the late-time
approach to the equilibrium.
