Stochastic inflation from quantum field theory and the parametric dependence of the effective noise amplitude

TL;DR

This paper derives an effective stochastic description of long-wavelength cosmological fluctuations from quantum field theory, emphasizing how the noise amplitude depends on parameters and influences cosmological correlations.

Contribution

It provides a first-principles derivation of the stochastic noise amplitude in inflationary dynamics, highlighting its parametric dependence and non-perturbative IR regulation.

Findings

Derived the effective stochastic evolution from quantum field theory.

Analyzed the parametric dependence of the noise amplitude.

Identified the role of noise amplitude in cosmological correlations.

Abstract

The non-linear dynamics of long-wavelength cosmological fluctuations may be phrased in terms of an effective classical, but stochastic evolution equation. The stochastic noise represents short-wavelength modes that continually redshift into the long-wavelength domain. The effective evolution may be derived from first principles quantum field theory in an expanding background, through a sequence of approximations calling for additional scrutiny. We perform such an analysis, putting particular emphasis on the amplitude of the stochastic noise, which ultimately determines the cosmological correlations and provides a non-perturbative IR regulator to the dynamics.