Perturbations in generalized Galileon theories

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.

This is a journal version of the article. The proof of the statement made in Section 3 has been considerably revised. The paper consists of 13 pages

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