Constraining some Horndeski gravity theories

We discuss two spherically symmetric solutions admitted by the Horndeski (or scalar-tensor) theory in the context of Solar System and astrophysical scenarios. One of these solutions is derived for Einstein-Gauss-Bonnet gravity, while the other originates from the coupling of the Gauss-Bonnet invariant with a scalar field. Specifically, we discuss the perihelion precession and the bending angle of light for these two different spherically symmetric spacetimes derived in Maeda and Dadhich [Phys. Rev. D 75, 044007 (2007)] and Sotiriou and Zhou [Phys. Rev. D 90, 124063 (2014)], respectively. The latter, in particular, applies only to black-hole spacetimes. We further delineate on the numerical bounds of relevant parameters of these theories from such computations.