Bounds on the Horndeski gauge-gravity coupling

The Horndeski gauge-gravity coupling is the leading non-minimal interaction between gravity and gauge bosons, and it preserves all the symmetries and the number of physical degrees of freedom of the standard model of particle physics and general relativity. In this paper we study the effects of the non-minimal interaction in astronomy and cosmology, and obtain upper bounds on the associated dimensionless coupling constant lambda. From the modification of equations of motion of gauge bosons applied to compact astronomical objects, we find upper bounds vertical bar lambda vertical bar less than or similar to 10(88), vertical bar lambda vertical bar less than or similar to 10(70) and vertical bar lambda vertical bar less than or similar to 10(81) from a black hole shadow, neutron stars and white dwarfs, respectively. The bound vertical bar lambda vertical bar less than or similar to 10(70) that is deduced from neutron stars is the strongest and provides twenty orders of magnitude improvement of the previously known best bound on this parameter. On the other hand, the effects of this term on modification of the gravitational Poisson equation lead to a weaker bound vertical bar lambda vertical bar less than or similar to 10(98). From the propagation of gravitational waves we also find vertical bar lambda vertical bar less than or similar to 10(119), which is even weaker.