Solution of the Dyson--Schwinger equation on de Sitter background in IR limit

TL;DR

This paper derives an analytical solution to the Dyson-Schwinger equation for scalar fields in de Sitter space, revealing how the Bunch-Davies vacuum evolves into a state with a flat Gibbons-Hawking density in the IR limit.

Contribution

It introduces an ansatz that simplifies the Dyson-Schwinger equation to a kinetic equation, providing new insights into vacuum relaxation in de Sitter space.

Findings

The Dyson-Schwinger equation reduces to a kinetic equation for principal series scalar fields.

The Bunch-Davies vacuum relaxes to a state with flat Gibbons-Hawking density.

The relaxation process occurs in the IR limit with adiabatic switching of coupling.

Abstract

We propose an ansatz which solves the Dyson-Schwinger equation for the real scalar fields in Poincare patch of de Sitter space in the IR limit. The Dyson-Schwinger equation for this ansatz reduces to the kinetic equation, if one considers scalar fields from the principal series. Solving the latter equation we show that under the adiabatic switching on and then off the coupling constant the Bunch-Davies vacuum relaxes in the future infinity to the state with the flat Gibbons-Hawking density of out-Jost harmonics on top of the corresponding de Sitter invariant out-vacuum.