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 references \cite{Maeda:2006hj} and \cite{Sotiriou:2014pfa} respectively. The later in particular, applies only to the black hole spacetimes. We further delineate on the numerical bounds of relevant parameters of these theories from such computations.