Suppression of matter couplings with a vector field in generalized Proca theories

TL;DR

This paper investigates how generalized Proca theories with various derivative interactions suppress matter couplings via the Vainshtein mechanism, ensuring compatibility with local gravity tests by analyzing vector field profiles around compact objects.

Contribution

It derives vector field profiles in generalized Proca theories with cubic, quartic, and sixth-order interactions, demonstrating suppression of longitudinal modes and consistency with gravity constraints.

Findings

Longitudinal vector modes are suppressed by the Vainshtein mechanism.

Models with cubic, quartic, and sixth-order interactions can satisfy local gravity constraints.

Quintic Galileon interactions do not admit regular solutions for rapidly decreasing matter density.

Abstract

We derive the profile of a vector field coupled to matter on a static and spherically symmetric background in the context of generalized Proca theories. The cubic Galileon self-interaction leads to the suppression of a longitudinal vector component due to the operation of the Vainshtein mechanism. For quartic and sixth-order derivative interactions, the solutions consistent with those in the continuous limit of small derivative couplings correspond to the branch with the vanishing longitudinal mode. We compute the corrections to gravitational potentials outside a compact body induced by the vector field in the presence of cubic, quartic, and sixth-order derivative couplings, and show that the models can be consistent with local gravity constraints under mild bounds on the temporal vector component. The quintic Galileon interaction does not allow regular solutions of the longitudinal mode for a rapidly decreasing matter density outside the body.