Massless Interacting Scalar Fields in de Sitter space

TL;DR

This paper introduces a novel method to compute two-point functions for massless $O(N)$ scalar fields in de Sitter space, effectively addressing infrared issues through a combined Euclidean zero mode treatment and perturbative expansion.

Contribution

The paper develops a systematic approach combining zero mode exact treatment and perturbative nonzero modes, enabling higher order calculations in coupling and large N limits.

Findings

Resummation leads to decay of correlation functions.

Results match known infrared approximations and large N limits.

Method allows systematic higher order corrections.

Abstract

We present a method to compute the two-point functions for an $O(N)$ scalar field model in de Sitter spacetime, avoiding the well known infrared problems for massless fields. The method is based on an exact treatment of the Euclidean zero modes and a perturbative one of the nonzero modes, and involves a partial resummation of the leading secular terms. This resummation, crucial to obtain a decay of the correlation functions, is implemented along with a double expansion in an effective coupling constant $\sqrt\lambda$ and in $1/N$. The results reduce to those known in the leading infrared approximation and coincide with the ones obtained directly in Lorentzian de Sitter spacetime in the large $N$ limit. The new method allows for a systematic calculation of higher order corrections both in $\sqrt\lambda$ and in $1/N$.