Nonlinear superhorizon curvature perturbation in generic single-field inflation

TL;DR

This paper develops a comprehensive nonlinear theory of superhorizon curvature perturbations for a broad class of single-field inflation models called G-inflation, extending linear results to second order in gradient expansion.

Contribution

It introduces a general nonlinear solution and a master evolution equation for curvature perturbations in G-inflation, surpassing previous models like k-inflation.

Findings

Derived a second-order nonlinear solution for metric and scalar field.

Established a simple master equation for large-scale curvature evolution.

Extended linear perturbation theory to nonlinear regime in G-inflation.

Abstract

We develop a theory of nonlinear cosmological perturbations on superhorizon scales for generic single-field inflation. Our inflaton is described by the Lagrangian of the form $W(X,\phi)-G(X,\phi)\Box\phi$ with $X=-\partial^{\mu}\phi\partial_{\mu}\phi/2$, which is no longer equivalent to a perfect fluid. This model is more general than k-inflation, and is called G-inflation. A general nonlinear solution for the metric and the scalar field is obtained at second order in gradient expansion. We derive a simple master equation governing the large-scale evolution of the nonlinear curvature perturbation. It turns out that the nonlinear evolution equation is deduced as a straightforward extension of the corresponding linear equation for the curvature perturbation on uniform $\phi$ hypersurfaces.