The Parametrized Post-Newtonian-Vainshteinian Formalism

TL;DR

This paper develops an extended Parameterized Post-Newtonian formalism, called PPNV, to analyze gravity theories with Vainshteinian corrections, enabling tests of their compatibility with solar system and strong-field data.

Contribution

It introduces the PPNV formalism with a dual-parameter expansion to handle Vainshteinian effects in modified gravity theories.

Findings

Framework applied to Cubic Galileon theory inside and outside the Vainshtein radius.

Provides a method to test the compatibility of Vainshteinian theories with observational data.

Establishes a systematic way to incorporate Vainshteinian corrections into post-Newtonian analysis.

Abstract

Light degrees of freedom that modify gravity on cosmological scales must be "screened" on solar system scales in order to be compatible with data. The Vainshtein mechanism achieves this through a breakdown of classical perturbation theory, as large interactions involving new degrees of freedom become important below the so-called Vainshtein radius. We begin to develop an extension of the Parameterized Post-Newtonian (PPN) formalism that is able to handle Vainshteinian corrections. We argue that theories with a unique Vainshtein scale must be expanded using two small parameters. In this Parameterized Post-Newtonian-Vainshteinian (PPNV) expansion, the primary expansion parameter that controls the PPN order is, as usual, the velocity $v$. The secondary expansion parameter, $\alpha$, controls the strength of the Vainshteinian correction and is a theory-specific combination of the Schwarzschild radius and the Vainshtein radius of the source that is independent of its mass. We present the general framework and apply it to Cubic Galileon theory both inside and outside the Vainshtein radius. The PPNV framework can be used to determine the compatibility of such theories with solar system and other strong-field data.