Screening fifth forces in generalized Proca theories

TL;DR

This paper investigates how generalized Proca theories with derivative self-interactions can suppress the longitudinal mode of a massive vector field via the Vainshtein mechanism, ensuring compatibility with solar-system gravity tests.

Contribution

It explicitly demonstrates the screening of the longitudinal mode in generalized Proca theories with cubic and quartic interactions, analyzing their effects on gravitational potentials and local gravity constraints.

Findings

Cubic interactions lead to effective Vainshtein screening of the longitudinal mode.

Quartic interactions with Ricci scalar coupling can eliminate the longitudinal mode.

Local gravity constraints are satisfied under mild parameter bounds.

Abstract

For a massive vector field with derivative self-interactions, the breaking of the gauge invariance allows the propagation of a longitudinal mode in addition to the two transverse modes. We consider generalized Proca theories with second-order equations of motion in a curved space-time and study how the longitudinal scalar mode of the vector field gravitates on a spherically symmetric background. We show explicitly that cubic-order self-interactions lead to the suppression of the longitudinal mode through the Vainshtein mechanism. Provided that the dimensionless coupling of the interaction is not negligible, this screening mechanism is sufficiently efficient to give rise to tiny corrections to gravitational potentials consistent with solar-system tests of gravity. We also study the quartic interactions with the presence of non-minimal derivative coupling with the Ricci scalar and find the existence of solutions where the longitudinal mode completely vanishes. Finally, we discuss the case in which the effect of the quartic interactions dominates over the cubic one and show that local gravity constraints can be satisfied under a mild bound on the parameters of the theory.