Perturbations in generalized multi-field inflation

TL;DR

This paper analyzes linear perturbations in general multi-field inflation models, deriving the second-order action, decomposing modes, and exploring their propagation speeds and contributions to curvature perturbations.

Contribution

It provides a comprehensive calculation of the second-order action for perturbations in general multi-field inflation models, including the propagation of entropy and adiabatic modes.

Findings

Entropy modes propagate at the speed of light.

Adiabatic mode propagates with an effective speed of sound.

Identifies entropy modes that source curvature perturbations.

Abstract

We study the linear perturbations of multi-field inflationary models governed by a Lagrangian which is a general function of the scalar fields and of a global kinetic term combining their spacetime gradients with an arbitrary field space metric. Our analysis includes k-inflation, DBI inflation and its multi-field extensions which have been recently studied. For this general class of models, we calculate the action to second order in the linear perturbations. We decompose the perturbations into an (instantaneous) adiabatic mode, parallel to the background trajectory, and entropy modes. We show that all the entropy modes propagate with the speed of light whereas the adiabatic mode propagates with an effective speed of sound. We also identify the specific combination of entropy modes which sources the curvature perturbation on large scales. We then study in some detail the case of two scalar fields: we write explicitly the equations of motion for the adiabatic and entropy modes in a compact form and discuss their quantum fluctuations and primordial power spectra.