Cosmological Correlators at Finite Coupling

TL;DR

This paper investigates the effects of finite coupling in quantum field theories on a de Sitter background, focusing on the $O(N)$ vector model at large $N$, and analyzes phase structure and four-point functions to test unitarity and analyticity.

Contribution

It extends large N techniques to de Sitter space, computes late-time four-point functions, and demonstrates the spectral density's properties, providing new insights into cosmological correlators.

Findings

Spontaneous symmetry breaking is suppressed by IR effects.

Late-time four-point functions have meromorphic spectral density.

Results support unitarity and analyticity in cosmological correlators.

Abstract

We study finite-coupling effects of QFT on a rigid de Sitter (dS) background taking the $O(N)$ vector model at large $N$ as a solvable example. Extending standard large $N$ techniques to the dS background, we analyze the phase structure and late-time four-point functions. Explicit computations reveal that the spontaneous breaking of continuous symmetries is prohibited due to strong IR effects, akin to flat two-dimensional space. Resumming loop diagrams, we compute the late-time four-point functions of vector fields at large $N$, demonstrating that their spectral density is meromorphic in the spectral plane and positive along the principal series. These results offer highly nontrivial checks of unitarity and analyticity for cosmological correlators.