A Lorentz Gauge Theory of Gravity

TL;DR

This paper introduces a Lorentz gauge theory of gravity where the metric is fixed, demonstrating that it can reproduce Schwarzschild and de Sitter solutions, and exploring its quantization and renormalizability.

Contribution

It presents a novel Lorentz gauge gravity theory with a non-dynamical metric, showing exact solutions and potential renormalizability.

Findings

Schwarzschild metric is an exact solution in the theory

De Sitter space is an exact vacuum solution

The theory can be power-counting renormalizable under certain conditions

Abstract

We present a Lorentz gauge theory of gravity in which the metric is not dynamical. Spherically symmetric weak field solutions are studied. We show that this solution contains the Schwarzschild spacetime at least to the first order of perturbation. Next, we present a special case of the theory. It is shown that the Schwarzschild metric is now an exact solution. Moreover, we show that the de Sitter space is an exact vacuum solution and as a result the theory is able to explain the expansion of the universe with no need for a dark energy. Within this special case, quantization of the theory is also studied. The basic Feynman diagrams are derived and renormalizability of the theory is studied using the power-counting method. We show that under a certain condition the theory is power-counting renormalizable.