On Resumming Inflationary Perturbations beyond One-loop

TL;DR

Inflationary scalar perturbations exhibit cumulative infrared effects that challenge perturbation theory. The authors analyze an $O(N)$ invariant scalar field with quartic self-interactions in de Sitter space using the in-in formalism and a large-$N$ 2PI resummation to capture IR physics non-perturbatively. They find a finite, non-perturbatively enhanced trispectrum with a characteristic enhancement factor ∼ $12π/√λ$, and identify a non-perturbative mass $m_{np}^2 ≈ (√{3λ}/(4π)) H^2$ that regulates IR and sets a finite correlation time; curvature perturbations also receive non-perturbative λ- and N-dependent corrections. These results provide a concrete, controlled framework for IR effects in self-interacting inflation and connect to stochastic approaches, improving predictions for non-Gaussianity from inflationary dynamics.

Abstract

It is well known that the correlation functions of a scalar field in a quasi-de Sitter space exhibit at the loop level cumulative infra-red effects proportional to the total number of e-foldings of inflation. Using the in-in formalism, we explore the behavior of these infra-red effects in the large N limit of an O(N) invariant scalar field theory with quartic self-interactions. By resumming all higher-order loop diagrams non-perturbatively, we show that the connected four-point correlation function, which is a signal of non-Gaussianity, is non-perturbatively enhanced with respect to its tree-level value.