de Sitter limit of inflation and nonlinear perturbation theory

TL;DR

This paper investigates the behavior of the nonlinear curvature perturbation in inflationary cosmology, deriving the fourth order action and analyzing its vanishing in the de Sitter limit to understand higher-order correlations.

Contribution

It systematically derives the fourth order action of the curvature perturbation and explores its implications for the de Sitter limit and higher-order correlation functions.

Findings

Fourth order action vanishes rapidly in the de Sitter limit

Extrapolation to n-th order action informs slow-roll order of n-point functions

Provides a systematic approach to nonlinear perturbation theory in inflation

Abstract

We study the fourth order action of the comoving curvature perturbation in an inflationary universe in order to understand more systematically the de Sitter limit in nonlinear cosmological perturbation theory. We derive the action of the curvature perturbation to fourth order in the comoving gauge, and show that it vanishes sufficiently fast in the de Sitter limit. By studying the de Sitter limit, we then extrapolate to the n'th order action of the comoving curvature perturbation and discuss the slow-roll order of the n-point correlation function.