Horndeski speed tests with scalar-photon couplings

TL;DR

This paper investigates how scalar-photon couplings in Horndeski theories affect the propagation speeds of gravitational and electromagnetic waves, revisiting constraints from neutron star merger observations and exploring theoretical implications of disformal relations.

Contribution

It demonstrates that certain Horndeski models can be disformally related to unit-speed gravitational wave theories and examines the impact of scalar-photon couplings on multi-messenger constraints.

Findings

Disformal relations can relate models with non-unit electromagnetic wave speed to those with unit gravitational wave speed.

Higher order scalar-photon couplings are incompatible with multi-messenger speed constraints.

Scalar-photon couplings influence the phenomenology of gravitational wave and electromagnetic wave propagation.

Abstract

We revisit multi-messenger constraints from neutron star mergers on the speed of propagation of gravitational and electromagnetic waves in Horndeski and beyond Horndeski theories. By considering non-trivial couplings between the dark energy field and the electromagnetic sector, the electromagnetic wave can propagate through the cosmological background at non-unit speed, altering the phenomenological constraints on its gravitational counterpart. In particular, we show that recent models derived from a Kaluza-Klein compactification of higher dimensional Horndeski models fall into a broader class of theories disformally related to those whose gravitational waves propagate with unit speed. This disformal equivalence can, however, be broken by the gravitational couplings to other sectors with interesting phenomenological consequences. We also consider higher order couplings between the scalar and the photon with second order field equations, and show that they are not compatible with constraints coming from multi-messenger speed tests and the decay of the gravitational wave.