Vector-tensor gravity from a broken gauge symmetry

Abstract

In this paper we present a Yang-Mills type gauge theory of vector-tensor gravity, where the tetrad, the spin connection and vector field are identified with components of the gauge field. This setup leads to a theory that in flat spacetime is contained in Generalized Proca theories, while in curved spacetime is closely related to beyond Generalized Proca. We solve for static and spherically symmetric space-time and show that there are two branches of solutions, one where the metric is asymptotically Schwarzschild even though there is a cosmological constant in the action, and another one where the metric is asymptotically (anti-)de Sitter. Also, we study the effect of the vector field on homogeneous and isotropic spacetimes, finding that it contributes to the accelerated expansion of the spacetime.