General Teleparallel Quadratic Gravity

TL;DR

This paper develops a comprehensive quadratic teleparallel gravity framework, analyzing its geometric foundations, gauge symmetries, and spectrum around Minkowski space to identify viable theories with potential physical relevance.

Contribution

It introduces a general quadratic parity-preserving teleparallel gravity theory, unifies known equivalents of General Relativity, and examines the spectrum for viability and gauge symmetries.

Findings

The linear spectrum includes two symmetric rank-2 fields and a 2-form.

Extra gauge symmetries are needed for viable theories.

The theory encompasses known teleparallel equivalents of GR.

Abstract

In this Letter we consider a general quadratic parity-preserving theory for a general flat connection. Imposing a local symmetry under the general linear group singles out the general teleparallel equivalent of General Relativity carrying both torsion and non-metricity. We provide a detailed discussion on the teleparallel equivalents of General Relativity and how the two known equivalents, formulated on Weitzenb\"ock and symmetric teleparallel geometries respectively, can be interpreted as two gauge-fixed versions of the general teleparallel equivalent. We then explore the viability of the general quadratic theory by studying the spectrum around Minkowski. The linear theory generally contains two symmetric rank-2 fields plus a 2-form and, consequently, extra gauge symmetries are required to obtain potentially viable theories.