On the fate of coupled flat directions during inflation

TL;DR

This paper studies how coupled scalar fields behave during inflation, showing that initial conditions and coupling influence fluctuation growth and equilibrium attainment, with a new formula for variance accounting for these effects.

Contribution

It introduces a general expression for the variance of coupled scalar fields during inflation, capturing both growth and equilibrium phases.

Findings

Initial expectation value can temporarily block fluctuation growth.

Fluctuations reach equilibrium if inflation lasts long enough.

Derived a novel formula for the variance of coupled fields.

Abstract

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.