Einstein-vector gravity, emerging gauge symmetry, and de Sitter bounce
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 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 bared 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 in the later time. 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.