Post-Newtonian parameter $\gamma$ for multiscalar-tensor gravity with a general potential

TL;DR

This paper calculates the post-Newtonian parameter gamma for multiscalar-tensor gravity with a general potential, providing a framework to test various models against experimental data like Cassini's measurements.

Contribution

It derives a general expression for gamma in multiscalar-tensor theories with arbitrary couplings and potential, extending previous single-field results and enabling broad model testing.

Findings

Gamma depends exponentially on distance from the source.

Bounds on two-scalar theories are estimated from Cassini data.

The formalism applies to diverse models like nonminimally coupled Higgs and nonlocal gravity.

Abstract

We compute the parametrized post-Newtonian parameter $\gamma$ in the case of a static point source for multiscalar-tensor gravity with completely general nonderivative couplings and potential in the Jordan frame. Similarly to the single massive field case $\gamma$ depends exponentially on the distance from the source and is determined by the length of a vector of non-minimal coupling in the space of scalar fields and its orientation relative to the mass eigenvectors. Using data from the Cassini tracking experiment, we estimate bounds on a general theory with two scalar fields. Our formalism can be utilized for a wide range of models, which we illustrate by applying it to nonminimally coupled Higgs SU(2) doublet, general hybrid metric-Palatini gravity, linear ($\Box^{-1}$) and quadratic ($\Box^{-2}$) nonlocal gravity.