Effective noise in a stochastic description of inflation

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.