Nonlinear perturbations of cosmological scalar fields with non-standard kinetic terms

TL;DR

This paper develops a covariant formalism to derive exact nonlinear evolution equations for scalar perturbations with non-standard kinetic terms in a two-field inflationary universe, generalizing linear theory and enabling analysis of complex models.

Contribution

It introduces a covariant approach to nonlinear perturbations with non-canonical kinetic terms, including a decomposition into adiabatic and entropy modes and a second-order expansion.

Findings

Derived exact nonlinear evolution equations for scalar perturbations.

Generalized the curvature perturbation to nonlinear regimes, showing its sourcing by entropy perturbations.

Provided a framework to analyze multifield Dirac-Born-Infeld inflation.

Abstract

We adopt a covariant formalism to derive exact evolution equations for nonlinear perturbations, in a universe dominated by two scalar fields. These scalar fields are characterized by non-canonical kinetic terms and an arbitrary field space metric, a situation typically encountered in inflationary models inspired by string theory. We decompose the nonlinear scalar perturbations into adiabatic and entropy modes, generalizing the definition adopted in the linear theory, and we derive the corresponding exact evolution equations. We also obtain a nonlinear generalization of the curvature perturbation on uniform density hypersurfaces, showing that on large scales it is sourced only by the nonlinear version of the entropy perturbation. We then expand these equations to second order in the perturbations, using a coordinate based formalism. Our results are relatively compact and elegant and enable one to identify the new effects coming from the non-canonical structure of the scalar fields Lagrangian. We also explain how to analyze, in our formalism, the interesting scenario of multifield Dirac-Born-Infeld inflation.