Parameterized post-Newtonian limit of Horndeski's gravity theory

摘要

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