Reviving Horndeski after GW170817 by Kaluza-Klein compactifications

TL;DR

This paper shows that certain Galileon theories derived from higher dimensions via Kaluza-Klein compactification naturally have luminal gravitational waves and are compatible with observational constraints, expanding the viable models of modified gravity.

Contribution

It demonstrates that 4D Galileons from higher-dimensional theories can evade GW speed constraints without fine tuning, broadening the class of viable modified gravity models.

Findings

4D Galileons from Kaluza-Klein compactification have luminal gravitational waves.

Some Galileon models previously ruled out are still viable.

Vainshtein screening applies to both gravity and electrodynamics in dense regions.

Abstract

The application of Horndeski theory/ Galileons for late time cosmology is heavily constrained by the strict coincidence in the speed of propagation of gravitational and electromagnetic waves. These constraints presuppose that the minimally coupled photon is not modified, not even at the scales where General Relativity (GR) may need modification. We find that the 4D Galileon obtained from a Kaluza-Klein compactification of its higher dimensional version is a natural simultaneous modification of GR and electromagnetism with automatically "luminal" gravitational waves. This property follows without any fine tuning of Galileon potentials for a larger class of theories than previously thought. In particular, the $G_4$ potential is not constrained by the speed test and $G_5$ may also be present. In other words, some Galileon models that have been ruled out since the event GW170817 are, in fact, not necessarily constrained if they arise in 4D from compactifications of their higher dimensional Galileon counterparts. Besides their compelling luminality, the resulting vector Galileons are naturally $U(1)$ gauge invariant. We also argue that the Vainshtein screening that allows to recover GR predictions for solar system tests is also at work for electrodynamics in the dense region of laboratory tests.