Einstein-Proca theory from the Einstein-Cartan formulation

TL;DR

This paper develops a gravity theory with a massive vector field derived from quadratic curvature, using Einstein-Cartan formulation to avoid ghosts and strong coupling issues, and explores implications for dark matter production.

Contribution

It introduces a novel Einstein-Cartan based gravity model with propagating torsion that naturally yields Einstein-Proca fields without instabilities.

Findings

Ghost and strong-coupling problems are avoided through nonlinear analysis.

The theory constrains Einstein-Proca model parameters.

Potential implications for fermionic dark matter production are discussed.

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.