Stochastic Inflation and Replica Field Theory

TL;DR

This paper applies statistical field theory methods to stochastic inflation, analyzing how different filtering techniques affect the power spectrum of long-wavelength fluctuations in de Sitter and power-law inflation models.

Contribution

It introduces a novel approach combining stochastic inflation with replica field theory, revealing how filter shape influences the infrared behavior of the power spectrum.

Findings

Infinite support filters lead to dimensional reduction phenomena.

Compact support filters yield a scale-invariant infrared power spectrum.

Filter-induced features decay rapidly, making the late-time spectrum filter-independent.

Abstract

We adopt methods from statistical field theory to stochastic inflation. For the example of a free test field in de Sitter and power-law inflation, the power spectrum of long-wavelength fluctuations is computed. We study its dependence on the shape of the filter that separates long from short wavelength modes. While for filters with infinite support the phenomenon of dimensional reductions is found on large super-horizon scales, filters with compact support return a scale-invariant power spectrum in the infra-red. Features of the power spectrum, induced by the filter, decay within a few e-foldings. Thus the late-time power spectrum is independent of the filter details.