Classicality of Stochastic Noise Away From Quasi-de Sitter Inflation

TL;DR

This paper derives exact noise amplitudes for a scalar field in inflationary backgrounds with various equations of state, showing classical stochastic behavior emerges beyond de Sitter space and depends on the equation of state parameter w.

Contribution

It provides exact expressions for noise amplitude in inflationary backgrounds with constant w, extending understanding beyond de Sitter space and analyzing the classicality conditions.

Findings

Classical stochastic behavior occurs for -5/3 < w < -1/3.

Noise amplitude depends on cutoff parameter σ, except near w ≈ -1.

Larger cutoff values become feasible as w approaches -1/3.

Abstract

It is well known that a coarse-grained scalar field living on a de~Sitter (dS) background exhibits classical stochastic behavior, driven by a noise whose amplitude is set by the Hubble constant $H$. The coarse-graining is achieved by discarding wave numbers larger than a cutoff $\sigma a H$ and demanding that $\sigma \ll 1$. Similar results hold for quasi-dS space, where the equation of state parameter $w$ is close to $-1$. Here we present exact expressions for the noise amplitude of a free massless field on an inflationary background with constant $w < -1/3$. We find that a classical stochastic behavior can emerge for $-5/3 < w < -1/3$. Furthermore, as we move away from $w = -1$ and approach $w = -1/3$, the constraint $\sigma \ll 1$ is relaxed and larger cutoffs ($\sigma \sim 1$) become feasible, too. However, in general the amplitude of the noise depends on $\sigma$, except in the quasi-dS regime $w \approx -1$.