Equivalence Principle Violation in Vainshtein Screened Two-Body Systems

TL;DR

This paper investigates how the Vainshtein screening mechanism in modified gravity theories leads to violations of the equivalence principle in two-body systems, resulting in observable mass-dependent deviations in orbital precession.

Contribution

It provides numerical analysis showing that screened bodies do not move as test particles, revealing a mass-dependent violation of the equivalence principle in Vainshtein screened systems.

Findings

Screening nearly cancels the Laplacian of the scalar field at the second body.

First derivative forces are reduced proportionally to (M_B/M_A)^{3/5}.

Earth-Moon precession deviations are approximately 4%.

Abstract

In massive gravity, galileon, and braneworld explanations of cosmic acceleration, force modifications are screened by nonlinear derivative self-interactions of the scalar field mediating that force. Interactions between the field of a central body ("A") and an orbiting body ("B") imply that body B does not move as a test body in the field of body A if the orbit is smaller than the Vainshtein radius of body B. We find through numerical solutions of the joint field at the position of B that the A-field Laplacian is nearly perfectly screened by the B self-field, whereas first derivative or net forces are reduced in a manner that scales with the mass ratio of the bodies as (M_B/M_A)^{3/5}. The latter causes mass-dependent reductions in the universal perihelion precession rate, with deviations for the Earth-Moon system at the ~4% level. In spite of universal coupling, which preserves the microscopic equivalence principle, the motion of macroscopic screened bodies depends on their mass providing in principle a means for testing the Vainshtein mechanism.