# The two-body potential of Vainshtein screened theories

## TL;DR

This paper investigates the two-body potential in Vainshtein screened theories, revealing that nonlinear effects can violate the Equivalence Principle and impact celestial orbits.

## Contribution

It provides the first analysis of two-body potentials in Vainshtein screening beyond spherical symmetry using an Effective One-Body approach.

## Key findings

- Vainshtein screening suppresses fifth forces in dense environments.
- Nonlinear dependence on mass ratio leads to Equivalence Principle violation.
- Potential impact on lunar orbit dynamics.

## Abstract

Adding a light scalar degree of freedom to General Relativity often induces a fifth force whose magnitude is strongly constrained by laboratory experiments and solar system tests. The Vainshtein screening mechanism ensures that the effects of this supplementary force are suppressed in dense environments. However, the field solution of theories exhibiting Vainshtein screening is only known in spherically symmetric situations. In this article we examine in different configurations the two-body potential energy of pointlike particles in a specific $P(X)$ theory with Vainshtein screening. We use ideas borrowed from the Effective One-Body approach of Buonanno and Damour in order to restrict the form of the solution. Our results indicate that, even if Vainshtein screening is also fully active in the equal-mass case, the nonlinear dependance of the two-body energy on the mass ratio implies a violation of the Equivalence Principle. We compute the contribution of this effect to the Moon orbit for generic theories equipped with Vainshtein screening.