Lorentz gauge theory as a model of emergent gravity

TL;DR

This paper introduces a Lorentz gauge gravity model within Riemann-Cartan geometry that features a unique Lagrangian with propagating spin one modes, positive-definite Hamiltonian, and potential for emergent Einstein gravity in the early universe.

Contribution

It proposes a novel Lorentz gauge gravity theory with a unique Lagrangian, propagating modes, and positive Hamiltonian, suggesting a mechanism for emergent gravity.

Findings

Unique Lagrangian admits propagating spin one modes.

Model has a positive-definite Hamiltonian despite R^2 Lagrangian.

Potential for a renormalizable quantum gravity theory.

Abstract

We consider a class of Lorentz gauge gravity theories within Riemann-Cartan geometry which admits a topological phase in the gravitational sector. The dynamic content of such theories is determined only by the contortion part of the Lorentz gauge connection. We demonstrate that there is a unique Lagrangian that admits propagating spin one mode in correspondence with gauge theories of other fundamental interactions. Remarkably, despite the R^2 type of the Lagrangian and non-compact structure of the Lorentz gauge group, the model possesses rather a positive-definite Hamiltonian. This has been proved in the lowest order of perturbation theory. This implies further consistent quantization and leads to renormalizable quantum theory. It is assumed that the proposed model describes possible mechanism of emergent Einstein gravity at very early stages of the Universe due to quantum dynamics of contortion.