Einstein-Vector Gravity, Emerging Gauge Symmetry and de Sitter Bounce

TL;DR

This paper develops Einstein-vector theories with ghost-free properties, exploring their applications in cosmology, black holes, and wormholes, revealing new mechanisms for dark energy and emergent gauge symmetry.

Contribution

It introduces a class of Einstein-vector theories with bilinear curvature couplings, demonstrating emergent gauge symmetry and diverse exact solutions in cosmology and gravity.

Findings

Vector field induces accelerated expansion without cosmological constant

Exact de Sitter bounce solutions are found

New black holes, wormholes, and domain walls are constructed

Abstract

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.