Effective noise in stochastic description of inflation

TL;DR

This paper analyzes the statistical properties of the noise field in stochastic inflation, showing its correlator depends on smoothing scale and differs from previous models using sharp cutoffs, impacting simulation accuracy.

Contribution

It provides a generalized calculation of the noise correlator for various smoothing functions, extending prior work that used sharp momentum cutoffs.

Findings

Noise correlator depends on smoothing scale

Results differ from sharp cutoff models

Applicable to a wide class of smoothing functions

Abstract

Stochastic description of inflationary spacetimes emulates the growth of vacuum fluctuations by an effective stochastic ``noise field'' which drives the dynamics of the volume-smoothed inflaton. We investigate statistical properties of this field and find its correlator to be a function of distance measured in units of the smoothing length. Our results apply for a wide class of smoothing window functions and are different from previous calculations by Starobinsky and others who used a sharp momentum cutoff. We also discuss the applicability of some approximate noise descriptions to simulations of stochastic inflation.