Long distance behavior of $O(N)$-model correlators in de Sitter space and the resummation of secular terms

TL;DR

This paper investigates the long-distance behavior of two-point functions in an interacting $O(N)$ scalar model in de Sitter space, demonstrating that after resummation, these functions vanish at large distances.

Contribution

It introduces a simplified double expansion method in $1/N$ and coupling, extending previous results to next-to-leading order and showing the vanishing of correlators at long distances.

Findings

Two-point functions vanish at long distances after resummation.

Extended analysis to next-to-leading order in $1/N$.

Method applicable to fields with negative squared-mass.

Abstract

We analyze the long distance behavior of the two-point functions for an interacting scalar $O(N)$ model in de Sitter spacetime. Following our previous work, this behavior is analyzed by analytic continuation of the Euclidean correlators, which are computed by treating the homogeneous zero mode exactly and using a partial resummation of the interactions between the zero and the non-zero modes. We focus on massless fields and present an alternative derivation of our method, which involves a double expansion in $1/N$ and the coupling constant of the theory. This derivation is simpler than the previous one and can be directly extended for fields with negative squared-mass. We extend our previous results by computing the long wavelength limit of the two-point functions at next-to-leading order in $1/N$ and at leading order in the coupling constant, which involves a further resummation of Feynman diagrams (needed when the two-point functions are analitically continued). We prove that, after this extra resummation, the two-point functions vanish in the long distance limit.