Properties of perturbations in beyond Horndeski theories

TL;DR

This paper examines the applicability of a known method for deriving quadratic actions in beyond Horndeski theories, finds it produces incorrect results, and proposes modifications to improve its validity.

Contribution

It identifies limitations of the DPSV approach in beyond Horndeski theories and suggests modifications to correctly obtain the quadratic action for scalar perturbations.

Findings

The DPSV method removes higher derivatives but yields incorrect quadratic actions.

Analysis reveals why the method fails in beyond Horndeski theories.

Proposed modifications aim to produce valid quadratic actions in these theories.

Abstract

We study whether the approach of Deffayet et al. (DPSV) can be adopted for obtaining a derivative part of quadratic action for scalar perturbations in beyond Horndeski theories about homogeneous and isotropic backgrounds. We find that even though the method does remove the second and higher derivatives of metric perturbations from the linearized Galileon equation, in the same manner as in the general Horndeski theory, it gives incorrect result for the quadratic action. We analyse the reasons behind this property and suggest the way of modifying the approach, so that it gives valid results.