Stochastic approach to inflation: Classicality conditions

The stochastic approach to inflation relies on one key assumption, the emergence of a long-wave classical field that drives the inflation and is subject to a shortwave classical noise. In this work we consider explicitly the potential that acts on the inflaton field, and analyze classicality conditions that must be satisfied to have an effective classical stochastic approach. When these hold, the dynamics is given by a two-dimensional classical Fokker-Planck equation. We develop some examples, already widely considered in different approaches, and find a very suggestive result, which is the damping of the quantum fluctuations by the effect of the inflaton interaction potential.