Stochastic Approach to Flat Direction during Inflation

TL;DR

This paper investigates the evolution of flat and non-flat directions during inflation using stochastic formalism, highlighting the roles of quantum noise, radiative corrections, and non-renormalizable terms in their dynamics.

Contribution

It introduces a numerical stochastic approach to analyze flat directions during inflation, emphasizing the impact of quantum noise and one-loop corrections without tree-level Hubble-induced mass.

Findings

Quantum noise influences flat direction evolution.

Blocking effects are suppressed by effective masses.

One-loop corrections and non-renormalizable terms are crucial.

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.