The role of vector fields in modified gravity scenarios

Abstract

Gravitational vector degrees of freedom typically arise in many examples of modified gravity models.We start to systematically explore their role in these scenarios,studying the effects of coupling gravitational vector and scalar degrees of freedom. Wefocus on set-ups that enjoy a Galilean symmetry in the scalar sector and an Abelian gauge symmetryin the vector sector. These symmetries, together with the requirement that the equations of motioncontain at most two space-time derivatives, only allow for a small number of operatorsin the Lagrangian for the gravitational fields. We investigatethe role of gravitational vector fields for two broad classes of phenomena that characterize modified gravity scenarios.The first is self-acceleration: we analyze in general terms the behavior of vector fluctuationsaround self-accelerating solutions, and show that vanishing kinetic terms of vector fluctuationslead to instabilities on cosmological backgrounds. The second phenomenon is the screening of long range fifth forces by means of Vainshtein mechanism. We showthat if gravitational vector fields are appropriately coupled to a spherically symmetric source,they can play an important role for defining the features of the background solution and the scale of the Vainshteinradius. Our general results can be applied to any concrete model of modified gravity, whose low-energyvector and scalar degrees of freedom satisfy the symmetry requirements that we impose.