Time-dependent, spherically symmetric background in Kaluza-Klein compactified Horndeski theory and the speed of gravity waves

TL;DR

This paper demonstrates that in certain Kaluza-Klein compactified Horndeski theories, gravitational and electromagnetic waves propagate at the same non-unit speed on time-dependent spherically symmetric backgrounds, challenging previous constraints.

Contribution

It proves the equality of gravitational and electromagnetic wave speeds in these theories and establishes stability conditions for solutions, broadening the viability of Horndeski models.

Findings

Gravitational and electromagnetic waves propagate at the same non-unit speed.

Theories with photon-Galileon couplings are not necessarily ruled out by GW170817.

Stability conditions for solutions are formulated within the model.

Abstract

We revisit the models recently derived from a Kaluza-Klein compactification of higher dimensional Horndeski theory, where the resulting electromagnetic sector features non-trivial couplings to Horndeski scalar. In particular, this class of theories admits the electromagnetic waves propagating at non-unit speed, which in turn allows to relax the constraints on Horndeski theories following from multi-messenger speed test. In this work we prove that both gravitational wave and its electromagnetic counterpart propagate at the same, although non-unit, speed above an arbitrarily time-dependent, spherically symmetric background within the theories in question. Hence, we support the statement that several subclasses of Horndeski theories are not necessarily ruled out after the GW170817 event provided the photon-Galileon couplings are allowed. We also formulate the set stability conditions for an arbitraty solution within the discussed theoretical setting.