Perturbations in generalized Galileon theories

TL;DR

This paper compares two methods for analyzing linear scalar perturbations in Horndeski theories, clarifies their relation, and derives a gauge-invariant quadratic action for perturbations in generalized Galileon models.

Contribution

It identifies additional terms in the DPSV approach, shows they vanish in certain gauges, and derives a gauge-invariant quadratic action for scalar perturbations in specific Galileon theories.

Findings

Additional terms in DPSV approach vanish in certain gauges.

Gauge-invariant quadratic action for scalar perturbations derived.

Connections between DPSV and KYY approaches established.

Abstract

We discuss the approaches by Deffayet et al. (DPSV) and Kobayashi et al. (KYY) to the analysis of linearized scalar perturbations about a spatially flat FLRW background in Horndeski theory. We identify additional, potentially important terms in the DPSV approach. However, these terms vanish upon a judicious gauge choice. We derive a gauge invariant quadratic action for metric and Galileon perturbations in $\mathcal{L}_3$ and $\mathcal{L}_3+\mathcal{L}_4$ theories and show that actions obtained in the DPSV and KYY approaches follow from this gauge invariant action in particular gauges.