We construct a class of Einstein-vector theories where the vector field couples bilinearly to the curvature polynomials of arbitrary order in such a way that only the Riemann tensor rather than its derivative enters the equations of motion. The theories can thus be ghost free. The $U(1)$ gauge symmetry may emerge in the vacuum and also in some weak-field limit. We focus on the two-derivative theory and study a variety of applications. We find that in this theory, the energy-momentum tensor of dark matter provides a position-dependent gauge-violating term to the Maxwell field. We also use the vector as an inflaton and construct cosmological solutions. We find that the expansion can accelerate without a bare cosmological constant, indicating a new candidate for dark energy. Furthermore, we obtain exact solutions of de Sitter bounce, generated by the vector which behaves like a Maxwell field at later times. We also obtain a few new exact black holes that are asymptotic to flat and Lifshitz spacetimes. In addition, we construct exact wormholes and Randall-Sundrum II domain walls.

• Received 24 November 2015

DOI:https://doi.org/10.1103/PhysRevD.93.044035