The de Sitter limit of inflation and non-linear perturbation theory

Abstract

We study the fourth-order action of the comoving curvature perturbation in an inflationaryuniverse in order to understand more systematically the de Sitter limit in non-linearcosmological perturbation theory. We derive the action of the curvature perturbation tofourth order in the comoving gauge, and show that it vanishes sufficiently fast inthe de Sitter limit. By studying the de Sitter limit, we then extrapolate to thenth-order action of the comoving curvature perturbation and discuss the slow-roll order of then-point correlation function.