Parameterized post-Newtonian limit of Horndeski's gravity theory

TL;DR

This paper analyzes the parameterized post-Newtonian limit of Horndeski's scalar-tensor gravity theory, deriving conditions for validity and calculating PPN parameters, with implications for observational tests and specific models like galileons and Higgs inflation.

Contribution

It provides the first comprehensive derivation of PPN parameters for the most general scalar-tensor theories with second-order field equations, including distance-dependent effects.

Findings

PPN parameters $eta(r)$ and $ extgamma(r)$ depend on interaction distance in general.

For massless scalar fields, PPN parameters are constant and can deviate from General Relativity.

Application to models like galileons and Higgs inflation shows potential observational signatures.

Abstract

We discuss the parameterized post-Newtonian (PPN) limit of Horndeski's theory of gravity, also known under the name generalized G-inflation or $\text{G}^2$-inflation, which is the most general scalar-tensor theory of gravity with at most second order field equations in four dimensions. We derive conditions on the action for the validity of the post-Newtonian limit. For the most general class of theories consistent with these conditions we calculate the PPN parameters $\gamma(r)$ and $\beta(r)$, which in general depend on the interaction distance $r$ between the gravitating mass and the test mass. For a more restricted class of theories, in which the scalar field is massless, we calculate the full set of PPN parameters. It turns out that in this restricted case all parameters are constants and that the only parameters potentially deviating from observations are $\gamma$ and $\beta$. We finally apply our results to a number of example theories, including galileons and different models of Higgs inflation.