Post-Newtonian parameters gamma and beta of scalar-tensor gravity with a general potential

Abstract

We calculate the PPN parameters gamma and beta for scalar-tensor gravity with a generic coupling function omega and scalar potential V in the Jordan conformal frame in the case of a static spherically symmetric source. Since the potential generally introduces a radial dependence to the effective gravitational constant as well as to gamma and beta, we discuss the issue of defining these PPN parameters and compare our expressions with previous calculations in simpler cases. We confront our results with current observational constraints on the values of gamma and beta and thus draw restrictions on the form of the functions omega and V around their asymptotic background values.