Weak-field regime of the generalized hybrid metric-Palatini gravity

In this work we explore the dynamics of the generalized hybrid metric-Palatini theory of gravity in the weak-field, slow-motion regime. We start by introducing the equivalent scalar-tensor representation of the theory, which contains two scalar degrees of freedom, and perform a conformal transformation to the Einstein frame. Linear perturbations of the metric in a Minkowskian background are then studied for the metric and both scalar fields. The effective Newton constant and the PPN parameter $\gamma$ of the theory are extracted after transforming back to the (original) Jordan frame. Two particular cases where the general method ceases to be applicable are approached separately. A comparison of these results with observational constraints is then used to impose bounds on the masses and coupling constants of the scalar fields.