Post-Newtonian Constraints on Scalar-Tensor Gravity

TL;DR

This paper develops a unified post-Newtonian framework to analyze scalar-tensor gravity theories, highlighting how the choice of formalism influences weak-field phenomenology and observational constraints.

Contribution

It provides analytical expressions for key parameters in scalar-tensor theories and compares metric and Palatini formalisms within a unified post-Newtonian approach.

Findings

Palatini $f( ilde{R})$ gravity matches general relativity in the post-Newtonian limit.

The formalism's impact on Solar-System tests is highly model-dependent.

Palatini non-minimal couplings can weaken local bounds due to Yukawa suppression.

Abstract

Solar-System constraints on a general scalar-tensor theory with generic non-minimal coupling function, non-canonical kinetic function, and scalar potential, are investigated in both the metric and Palatini formalisms. A unified post-Newtonian treatment is developed, yielding analytical expressions for the effective scalar mass, the effective gravitational coupling, and the parametrised post-Newtonian parameters $\gamma$ and $\beta$. The results show explicitly how the choice of variational principle affects the weak-field phenomenology. Comparison with Solar-System observations, primarily the Cassini bound on $\gamma$, indicates that the observational impact of the formalism is strongly model dependent. Generic non-minimally coupled scalar fields may satisfy significantly weaker local bounds in the Palatini case because of stronger Yukawa suppression, whereas in Brans-Dicke gravity the differences are typically small and become appreciable only in restricted regions of parameter space. For the point-particle source considered here, Palatini $f(\hat{R})$ gravity reproduces the general-relativistic exterior post-Newtonian limit, unlike metric $f(R)$ gravity.