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 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 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.