Unequal time correlators of stochastic scalar fields in de Sitter space

TL;DR

This paper investigates the behavior of quantum fluctuations of a scalar field in de Sitter space by employing a stochastic effective theory, computing unequal-time correlators through perturbative and nonperturbative methods, and revealing underlying symmetries and relations.

Contribution

It introduces a supersymmetric stochastic framework to compute unequal-time correlators of scalar fields in de Sitter space, including high-order perturbative and nonperturbative analyses, and derives new spectral and fluctuation-dissipation relations.

Findings

Computed unequal-time correlators up to three-loop order.

Established a nonperturbative $1/N$ expansion at next-to-leading order.

Derived a spectral representation and fluctuation-dissipation relation for the scalar field.

Abstract

The quantum fluctuations of a test scalar field on superhorizon scale in de Sitter spacetime can be described by an effective one-dimensional stochastic theory corresponding to a particular class of nonequilibrium dynamical systems known as the model A. Using the formulation of the latter in terms of a supersymmetric field theory, we compute various unequal-time correlators at large (superhorizon) time separations and compare with existing quantum field theory computation. This includes perturbative calculations, pushed here up to three-loop order, and a nonperturbative $1/N$ expansion at next-to-leading order. Exploiting the supersymmetry of the stochastic theory, we also derive a spectral representation of the field correlators and a fluctuation-dissipation relation for the infrared modes of the scalar field in de Sitter spacetime.