Gravity as a Gauge Theory of Translations

TL;DR

This paper proposes a gauge theory approach to gravity based on the group of isometries of maximally symmetric spaces, extending the idea of Einstein gravity as a gauge theory of translations.

Contribution

It introduces the concept of minimal tetrads and develops a gauge theory framework for gravity that includes a cosmological constant.

Findings

Derives Einstein gravity as a gauge theory of translations in vacuum.

Extends gauge theory approach to maximally symmetric spaces with cosmological constant.

Provides a geometric interpretation of gravity using isometries and tetrads.

Abstract

The Poincar\'e group can be interpreted as the group of isometries of a minkowskian space. This point of view suggests to consider the group of isometries of a given space as the suitable group to construct a gauge theory of gravity. We extend these ideas to the case of maximally symmetric spaces to reach a realistic theory including the presence of a cosmological constant. Introducing the concept of "minimal tetrads" we deduce Einstein gravity in the vacuum as a gauge theory of translations.