Infrared dynamics in de Sitter space from Schwinger-Dyson equations

TL;DR

This paper analyzes the infrared behavior of scalar fields in de Sitter space using Schwinger-Dyson equations, revealing how resummation of self-energy insertions leads to well-defined power laws and nonperturbative effects.

Contribution

It provides an exact analytical solution to the Schwinger-Dyson equations for infrared momenta, demonstrating the resummation of infrared logarithms into power laws in de Sitter space.

Findings

Infrared logarithms are resummed into power laws.

The correlator shows a superposition of free-field-like power laws.

Mass and field-strength renormalizations are nonperturbative for zero tree-level mass.

Abstract

We study the two-point correlator of an O(N) scalar field with quartic self-coupling in de Sitter space. For light fields in units of the expansion rate, perturbation theory is plagued by large logarithmic terms for superhorizon momenta. We show that a proper treatment of the infinite series of self-energy insertions through the Schwinger-Dyson equations resums these infrared logarithms into well defined power laws. We provide an exact analytical solution of the Schwinger-Dyson equations for infrared momenta when the self-energy is computed at two-loop order. The obtained correlator exhibits a rich structure with a superposition of free-field-like power laws. We extract mass and field-strength renormalization factors from the asymptotic infrared behavior. The latter are nonperturbative in the coupling in the case of a vanishing tree-level mass.