Post-Newtonian parameters $\ensuremath{\gamma}$ and $\ensuremath{\beta}$ of scalar-tensor gravity with a general potential

Post-Newtonian parameters $γ$ and $β$ of scalar-tensor gravity with a general potential

Manuel Hohmann, Laur Järv, Piret Kuusk, and Erik Randla

Phys. Rev. D 88, 084054 – Published 29 October 2013; Erratum Phys. Rev. D 89, 069901 (2014)

Abstract

We calculate the parametrized post-Newtonian parameters $γ$ and $β$ for scalar-tensor gravity with a generic coupling function $ω$ 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 $γ$ and $β$ , we discuss the issue of defining these parametrized post-Newtonian parameters and compare our expressions with previous calculations in simpler cases. We confront our results with current observational constraints on the values of $γ$ and $β$ and thus draw restrictions on the form of the functions $ω$ and $V$ around their asymptotic background values.