Classicality of stochastic noise away from quasi-de Sitter inflation

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 σaH and demanding that σ ≪ 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 σ ≪ 1 is relaxed and larger cutoffs ( σ ∼ 1) become feasible, too. However, in general the amplitude of the noise depends on σ , except in the quasi-dS regime w ≈ -1.