Cosmological Correlators in massless ${\phi}^4$-theory and the Method of Regions

TL;DR

This paper introduces the method-of-region expansion to efficiently compute the late-time behavior of cosmological correlators in de Sitter space, addressing challenges in loop corrections for quantum fields during inflation.

Contribution

It develops and demonstrates a novel method-of-region expansion technique tailored for cosmological correlators, facilitating late-time limit calculations in de Sitter space.

Findings

Method-of-region expansion effectively extracts late-time limits.

Application to in-in correlators reveals insights into anomalous dimensions.

Illustrated with examples for massless scalar fields in de Sitter.

Abstract

The calculation of loop corrections to the correlation functions of quantum fields during inflation or in the de~Sitter background presents greater challenges than in flat space due to the more complicated form of the mode functions. While in flat space highly sophisticated approaches to Feynman integrals exist, similar tools still remain to be developed for cosmological correlators. However, usually only their late-time limit is of interest. We introduce the method-of-region expansion for cosmological correlators as a tool to extract the late-time limit, and illustrate it with several examples for the interacting, massless, minimally coupled scalar field in de~Sitter space. In particular, we consider the in-in correlator $\langle\phi^2(\eta,q)\phi(\eta,k_1)\phi(\eta,k_2)\rangle$, whose region structure is relevant to anomalous dimensions and matching coefficients in Soft de Sitter effective theory.