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.

对于具有导数自相互作用的大质量矢量场，规范不变性的破缺使得除了两个横向模式之外，还能传播一个纵向模式。我们考虑在弯曲时空下具有二阶运动方程的广义普罗卡理论，并研究矢量场的纵向标量模式在球对称背景下如何产生引力作用。我们明确表明，三次方阶的自相互作用通过温施泰因机制导致纵向模式受到抑制。如果相互作用的无量纲耦合不可忽略，这种屏蔽机制足够有效，能够对引力势产生微小修正，这与太阳系的引力测试相符。我们还研究了与里奇标量存在非最小导数耦合的四次方相互作用，并发现纵向模式完全消失的解的存在性。最后，我们讨论了四次方相互作用的影响超过三次方相互作用的情况，并表明在理论参数的适度限制下，可以满足局部引力约束。