Screening fifth forces in generalized Proca theories
  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.
