Taming the infrared in de Sitter space: autonomous equations, stochastic approach, and Borel resummation

TL;DR

This paper develops methods to handle divergent series in quantum field theory in de Sitter space, using autonomous equations, stochastic approaches, and Borel resummation to improve correlation function calculations.

Contribution

It introduces autonomous equations for finite-time correlation functions, applies Borel resummation techniques, and offers a new derivation via Schwinger-Dyson equations, advancing non-perturbative analysis.

Findings

Autonomous equations approximate correlation function evolution well.

Borel resummation improves agreement with stochastic results.

New derivation of autonomous equations from Schwinger-Dyson truncation.

Abstract

We investigate the divergent perturbative series of correlation functions for a massless, self-interacting scalar field in de Sitter space. First, we use our previously proposed method of autonomous equations to obtain finite time-dependent functions, and show that these functions approximate the time evolution of the correlation functions of the stochastic theory reasonably well. Second, we apply the technique of autonomous equations to the Borel-Le Roy transforms of correlation functions, and use solutions of these equations to perform Borel resummation. The results match the time evolution obtained in the stochastic picture substantially better. In addition, we propose an alternative method for extracting perturbative coefficients and provide a new derivation of our autonomous equation by truncating a system of Schwinger-Dyson-type differential equations.