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 Weitzenböck 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.
Highlights
One of the most beautiful properties of General Relativity (GR) is its intimate alliance with the geometry of spacetime
We provide a detailed discussion on the teleparallel equivalents of General Relativity and how the two known equivalents, formulated on Weitzenböck and symmetric teleparallel geometries respectively, can be interpreted as two gauge-fixed versions of the general teleparallel equivalent
The singular nature of General Teleparallel Equivalent of GR (GTEGR) has been revealed to be a complete gauging of the global G L(4, R) symmetry enjoyed by the general inertial connection
Summary
One of the most beautiful properties of General Relativity (GR) is its intimate alliance with the geometry of spacetime. The goal of this Letter is to extend previous studies in the literature on teleparallel geometries by allowing both torsion and non-metricity while keeping a trivial curvature, so the only constraint we impose is This condition fixes the connection to be a pure G L(4, R) gauge ( called inertial connection) so that it can be expressed in terms of an arbitrary α β. The latter would contribute second derivatives of the metric so they can be disregarded at the considered order, while the former would again contribute a total derivative plus terms already included in the T 2 and mixed T Q sectors This is so because the only dimension 2 operator involving derivatives and the torsion is ∇μ T μ, so if we expand the connection into Levi-Civita plus the disformation (that is proportional to the torsion and the non-metricity), we generate a total derivative plus the. T 2 and T Q terms aforementioned and, it would be redundant
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