Light fields in various patches of de Sitter space-time

TL;DR

This paper investigates the long-term behavior of light quantum fields in de Sitter space-time by deriving and solving Dyson-Schwinger equations to understand how initial states evolve under infrared effects in different patches of de Sitter space.

Contribution

It derives a Dyson-Schwinger equation for light fields in de Sitter space and analyzes the evolution of initial states considering infrared loop corrections in various patches.

Findings

Initial states evolve towards a specific destiny at future infinity.

Infrared loop effects significantly influence the long-term behavior of light fields.

Different patches of de Sitter space exhibit distinct evolution patterns for quantum fields.

Abstract

We start with the consideration of the loop effects for light fields with non-zero mass in the expanding Poincar\'e patch of de Sitter space-time. We derive the Dyson-Schwinger equation, which sums up the leading infrared (growing with time) loop corrections in certain limit for small initial perturbations above the Bunch-Davies state. The solution of this equation shows the destiny of the initial state at the future infinity. Then we discuss the case of the contracting Poincar\'e patch and global de Sitter space-time and briefly the case of different initial conditions in the expanding Poincar\'e patch.