The role of translational invariance in non linear gauge theories of gravity

TL;DR

This paper investigates how translational invariance influences the internal structure of tetrads in a non-linear gauge theory of gravity, revealing Minkowskian coordinates as dynamical Goldstone bosons and establishing a covariant expansion framework.

Contribution

It introduces a covariant expansion method in non-linear gauge gravity theories, highlighting the role of Minkowskian coordinates as Goldstone bosons of translations.

Findings

Minkowskian coordinates act as Goldstone bosons.

A critical length for covariant expansion is derived.

The zeroth order metric is maximally symmetric.

Abstract

The internal structure of the tetrads in a Poincar\'e non linear gauge theory of gravity is considered. Minkowskian coordinates becomes dynamical degrees of freedom playing the role of Goldstone bosons of the translations. A critical length allowing a covariant expansion similar to the weak field approach is deduced, the zeroth order metric being maximally symmetric (Minkowskian in some cases).