A Generalized Gauge Theory of Gravity

TL;DR

This paper introduces a generalized gauge theory of gravity that extends traditional frameworks by incorporating a new gauge transformation, resulting in a tensor gauge field and connections to Einstein-Hilbert and scalar-tensor theories.

Contribution

It proposes a novel gravitational gauge theory invariant under additional transformations, deriving Einstein-Hilbert action and scalar-tensor Lagrangian from this framework.

Findings

The gauge field is a second-rank tensor.

Einstein-Hilbert action derived from the gauge theory.

Provides a Lagrangian for scalar-tensor gravity.

Abstract

In this paper, we discuss a gravitational theory based on the generalized gauge field. Our Lagrangian is invariant not only under local Lorentz transformation and the ordinary gauge transformation but also under a new gauge transformation. We show that the gauge field associated with this new transformation is a second-rank tensor field and that the Einstein-Hilbert term can be derived from our Lagrangian when the gauge field has a vacuum expectation value. We also show that our model provides a Lagrangian for the scalar-tensor theory.