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

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 in the parity odd sector above an arbitrary solution. In this general setting we derive speeds of propagation in both radial and angular directions for the only dynamical degree of freedom in the parity odd sector. We also briefly comment on the propagation speeds of the parity even modes over a dynamical, spherically symmetric background. In particular, we demonstrate 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.