The Parameterized Post-Newtonian-Vainshteinian formalism for the Galileon field

TL;DR

This paper extends the PPN formalism to include Vainshtein screening, applying it to Quartic and Quintic Galileon theories, revealing new potentials and behaviors that could be tested observationally.

Contribution

It introduces the PPNV formalism to analyze Galileon theories, providing new potentials and insights into screening effects at different orders.

Findings

New PPNV potentials for Quartic Galileon in screened and un-screened regions

Vainshtein screening absent at Newtonian order in Quintic Galileon

Theories behave like Brans-Dicke at Newtonian order in the Quintic case

Abstract

Recently, an extension to the Parameterized Post-Newtonian (PPN) formalism has been proposed. This formalism, the Parameterized 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 parameterized approaches to the effects of gravity beyond General Relativity. In the Quartic case, we find new PPNV potentials for both screened and un-screened 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.