Stochastic approach to gravitational waves from inflation

TL;DR

This paper develops a stochastic framework for modeling the superhorizon dynamics of inflationary gravitational waves, providing formulas for noise and drift that depend on specific cosmological scenarios, including non-standard phases.

Contribution

It introduces a novel coarse-graining and stochastic description for tensor modes during inflation, applicable to various cosmological models and phases.

Findings

Derived stochastic Fokker-Planck equations for tensor modes.

Applied formulas to de Sitter, power-law, and non-attractor inflation.

Analyzed effects of horizon crossing and superhorizon mode production.

Abstract

We propose a coarse-graining procedure for describing the superhorizon dynamics of inflationary tensor modes. Our aim is to formulate a stochastic description for the statistics of spin-2 modes which seed the background of gravitational waves from inflation. Using basic principles of quantum mechanics, we determine a probability density for coarse-grained tensor fields, which satisfies a stochastic Fokker-Planck equation at superhorizon scales. The corresponding noise and drift are computable, and depend on the cosmological system under consideration. Our general formulas are applied to a variety of cosmological scenarios, also considering cases seldom considered in the context of stochastic inflation, and which are important for their observational consequences. We start obtaining the expected expressions for noise and drift in pure de Sitter and power-law inflation, also including a discussion of effects of non-attractor phases. We then apply our methods to describe scenarios with a transition from inflation to standard cosmological eras of radiation and matter domination. We show how the interference between modes flowing through the cosmological horizon, and modes spontaneously produced at superhorizon scales, can affect the stochastic evolution of coarse-grained tensor quantities. In appropriate limits, we find that the corresponding spectrum of tensor modes at horizon crossing matches with the results of quantum field theory calculations, but we also highlight where differences can arise.