Post-Newtonian Constraints on Scalar-Tensor Gravity

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 ${\hat{I}}^3$ and ${\hat{I}}^2$. 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 ${\hat{I}}^3$, 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.

43 pages, 4 figures, 1 table, 5 appendices. Author-Accepted Manuscript

Topics & keywords

References in corpus (2)

• Resolving the Planck-DESI tension by nonminimally coupled quintessence
• Non-minimally coupled gravity constraints from DESI DR2 data