Recently, an extension to the parametrized post-Newtonian (PPN) formalism has been proposed. This formalism, the parametrized post-Newtonian-Vainshteinian (PPNV) formalism, is well suited to theories which exhibit Vainshtein screening of scalar fields. In this paper we apply the PPNV formalism to the quartic and quintic Galileon theories for the first time. As simple generalizations of standard scalar-tensor field theories they are important guides for the generalization of parametrized approaches to the effects of gravity beyond general relativity. In the quartic case, we find new PPNV potentials for both screened and unscreened regions of spacetime, showing that in principle these theories can be tested. In the quintic case we show that Vainshtein screening does not occur to Newtonian order, meaning that the theory behaves as Brans-Dicke to this order, and we discuss possible higher order effects.

• Received 7 November 2018

DOI:https://doi.org/10.1103/PhysRevD.99.084009