Physical momentum representation of scalar field correlators in de Sitter space

TL;DR

This paper introduces a novel momentum-based approach to compute scalar field correlators in de Sitter space, leveraging symmetries and nonequilibrium techniques for simplified analysis and potential numerical applications.

Contribution

It develops a new momentum representation for scalar correlators in de Sitter space that simplifies calculations and preserves diagrammatic rules, enabling both analytical and numerical studies.

Findings

Two-point functions depend on two physical momenta.

Schwinger-Dyson equations become momentum flow equations.

Method is suitable for analytical and numerical applications.

Abstract

We propose a new approach to compute correlators of quantum fields in de Sitter space. It is based on nonequilibrium field theory techniques, and exploits de Sitter symmetries so as to partially reduce the number of independent variables of n-point functions in a manner that preserves the usefulness of a momentum representation, e.g., for writing spatial convolution integrals as simple products. In this representation, the two-point function of a scalar field only depends on two physical momenta, and the corresponding Schwinger-Dyson evolution equations take the form of momentum flow equations. Moreover, standard diagrammatic rules can be entirely formulated in this representation. The method is suitable for analytical approximations as well as numerical implementations. In forthcoming publications, we apply it to resum infrared logarithmic terms appearing in the perturbative calculation of vertex and correlation functions.