Lorentz gauge theory as a model of emergent gravity

We consider a class of Lorentz gauge gravity theories within Riemann-Cartan geometry that 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 noncompact 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.