Einstein-Proca theory from the Einstein-Cartan formulation

Abstract

We construct a theory of gravity in which a propagating massive vector field arises from a quadratic curvature invariant. The Einstein-Cartan formulation and a partial suppression of torsion ensure the absence of ghost and strong-coupling problems, as we prove with nonlinear Lagrangian and Hamiltonian analysis. Augmenting General Relativity with a propagating torsion vector, our theory provides a purely gravitational origin of Einstein-Proca models and constrains their parameter space. As an outlook to phenomenology, we discuss the gravitational production of fermionic dark matter.

Comments: 13 pages, 5 figures, 3 appendices; v2: improved presentation and more detailed discussion of non-trivial effect of multipliers, matches published version