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

TL;DR

This work develops a covariant, fully nonlinear framework for two-field inflation with non-canonical kinetic terms and a general field-space metric. By decomposing perturbations into adiabatic and entropy modes, it derives exact evolution equations and a nonlinear curvature perturbation, demonstrating that on large scales the curvature is sourced only by the nonlinear entropy perturbation. The authors also provide a second-order expansion and translate the results into the standard coordinate-based approach, recovering known linear results and unveiling new nonlinear effects tied to the kinetic structure. The formalism is particularly suited to string-inspired models, including multifield DBI inflation, and offers compact, tractable expressions to study non-Gaussianities and mode conversion in complex inflationary scenarios.

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.