Gradient expansion approach to nonlinear superhorizon perturbations II -- a single scalar field --

TL;DR

This paper develops a nonlinear perturbation framework for a single scalar field universe on super-horizon scales using gradient expansion, explicitly deriving second-order corrections relevant for non-slowroll inflation models.

Contribution

It formulates a general solution for nonlinear super-horizon perturbations including second-order gradient corrections in a single scalar field context.

Findings

Derived the general solution valid to O(ε^2) including scalar and tensor modes.

Explicitly obtained second-order correction terms to the nonlinear curvature perturbation.

Applicable to models with non-slowroll stages during inflation.

Abstract

We formulate nonlinear perturbations of a scalar field dominated universe on super-horizon scales. We consider the case of a single scalar field. We take the gradient expansion approach. We adopt the uniform Hubble slicing and derive the general solution valid to $O(\epsilon^2)$, where $\epsilon$ is the expansion parameter associated with a spatial derivative, which includes both the scalar and tensor modes. In particular, the $O(\epsilon^2)$ correction terms to the nonlinear curvature perturbation, which become important in models with a non-slowroll stage during inflation, are explicitly obtained.