Stochastic approach to flat direction during inflation

Abstract

We revisit the time evolution of a flat and non-flat direction system during inflation.In order to take into account quantum noises in the analysis,we base on stochastic formalism and solve coupled Langevin equations numerically.We focus on a class of models in which tree-level Hubble-induced mass is not generated.Although the non-flat directions can block the growth of the flat direction's variance in principle,the blocking effects are suppressed by the effective masses of the non-flat directions.We find that the fate of the flat direction during inflation is determined by one-loop radiative corrections and non-renormalizable terms as usually considered,if we remove the zero-point fluctuation from the noise terms.