Linear stability of a time-dependent, spherically symmetric background in beyond Horndeski theory and the speed of gravity waves

TL;DR

This paper investigates the linear stability and propagation speeds of gravity waves in a spherically symmetric, time-dependent background within beyond Horndeski theories, revealing conditions under which gravity waves travel at luminal speeds.

Contribution

It derives stability conditions and propagation speeds for gravity waves in beyond Horndeski theories on dynamic backgrounds, extending previous static analyses.

Findings

Gravity waves can propagate at the speed of light in certain beyond Horndeski models.

Stability conditions for high-energy perturbations are formulated.

Luminal gravity wave speeds are maintained in specific theory subclasses.

Abstract

We address a dynamical, spherically symmetric background in beyond Horndeski theory and formulate a set of linear stability conditions for high energy perturbation modes above an arbitrary solution. In this general setting we derive speeds of propagation in both radial and angular directions for gravity waves and compare them with the speed of light in the case of minimally coupled photon. In particular, we find that the class of beyond Horndeski theories, which satisfy the equality of gravity waves' speed to the speed of light over a cosmological background, feature gravity waves propagating at luminal speeds above a time-dependent inhomogeneous background as well.