Dynamical variables in Gauge-Translational Gravity

TL;DR

This paper develops a gauge theory framework for gravity based on the isometry group of maximally symmetric spaces, emphasizing the role of translations and nonlinear realizations to identify dynamical variables.

Contribution

It introduces a gauge-theoretic model of gravity rooted in the isometry group, highlighting the significance of nonlinear realizations and translation symmetries.

Findings

Gravity modeled as a gauge theory of translations

Dynamical variables simplified to a diagonal matrix at first order

Non-diagonal elements contribute only at higher orders

Abstract

Assuming that the natural gauge group of gravity is given by the group of isometries of a given space, for a maximally symmetric space we derive a model in which gravity is essentially a gauge theory of translations. Starting from first principles we verify that a nonlinear realization of the symmetry provides the general structure of this gauge theory, leading to a simple choice of dynamical variables of the gravity field corresponding, at first order, to a diagonal matrix, whereas the non-diagonal elements contribute only to higher orders.