Nonlinear superhorizon perturbations of non-canonical scalar field

TL;DR

This paper develops a comprehensive non-linear perturbation theory for scalar fields with general Lagrangians on superhorizon scales, enabling analysis of non-Gaussianities in models like DBI inflation.

Contribution

It introduces a second-order gradient expansion framework for non-canonical scalar fields, extending previous linear or canonical approaches.

Findings

General solutions for superhorizon perturbations in scalar fields with $P(X,\phi)$.

Applicable to DBI inflation and perfect fluids with arbitrary equations of state.

Framework facilitates studying non-Gaussianities beyond linear order.

Abstract

We develop a theory of non-linear cosmological perturbations at superhorizon scales for a scalar field with a Lagrangian of the form $P(X,\phi)$, where $X=-\partial^{\mu}\phi\partial_{\mu}\phi$ and $\phi$ is the scalar field. We employ the ADM formalism and the spatial gradient expansion approach to obtain general solutions valid up to the second order in the gradient expansion. This formulation can be applied to, for example, DBI inflation models to investigate superhorizon evolution of non-Gaussianities. With slight modification, we also obtain general solutions valid up to the same order for a perfect fluid with a general equation of state $P=P(\rho)$.