Resummation of infrared logarithms in de Sitter space via Dyson-Schwinger equations: the ladder-rainbow approximation

TL;DR

This paper investigates the infrared behavior of a massless scalar field in de Sitter space, demonstrating that nonperturbative resummation via Dyson-Schwinger equations reveals decay in the two-point function, unlike perturbative series.

Contribution

It applies Dyson-Schwinger equations in the ladder-rainbow approximation to nonperturbatively resum infrared logarithms in de Sitter space.

Findings

Perturbative series is singular and secular in the infrared.

Nonperturbative resummation leads to decay of the two-point function.

Asymptotic analysis confirms the decay behavior.

Abstract

We study the infrared (large separation) behavior of a massless minimally coupled scalar quantum field theory with a quartic self interaction in de Sitter spacetime. We show that the perturbation series in the interaction strength is singular and secular, i.e. it does not lead to a uniform approximation of the solution in the infrared region. Only a nonperturbative resummation can capture the correct infrared behavior. We seek to justify this picture using the Dyson-Schwinger equations in the ladder-rainbow approximation. We are able to write down an ordinary differential equation obeyed by the two-point function and perform its asymptotic analysis. Indeed, while the perturbative series-truncated at any finite order-is growing in the infrared, the full nonperturbative sum can be decaying.