Equivalence Principle Violation in Vainshtein Screened Two-Body Systems

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.

18 pages, 9 figures; accepted version, corrected typos, added argument in Sec.IIA

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• Covariant Galileon
• Equivalence Principle Implications of Modified Gravity Models
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• Constructing stabilized brane world models in five-dimensional Brans-Dicke theory
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• Horndeski theory and beyond: a review
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• Testing Brans-Dicke Gravity with Screening by Scalar Gravitational Wave Memory
• Effective field theory of modified gravity on the spherically symmetric background: leading order dynamics and the odd-type perturbations
• The Parametrized Post-Newtonian-Vainshteinian Formalism
• Galileons and strong gravity
• The two-body potential of Vainshtein screened theories
• Equivalence Principle Violation in Weakly Vainshtein-Screened Systems
• Vainshtein screening for slowly rotating stars
• Two-body problem in theories with kinetic screening
• Dynamical simulations of colliding superconducting strings