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General Teleparallel Quadratic Gravity

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arxiv 1909.09045 v1 pith:6AANM2GZ submitted 2019-09-19 gr-qc

Jose Beltrán Jiménez , Lavinia Heisenberg , Damianos Iosifidis , Alejandro Jiménez-Cano , Tomi S. Koivisto This is my paper · ORCID
classification gr-qc
keywords generalteleparallelquadratictheoryequivalentequivalentslinearrelativity
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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.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Neutron stars in $f(\mathbb{Q})$ gravity

    gr-qc 2025-12 conditional novelty 6.0 of 10

    For f(Q)=Q+αQ² and f(Q)=Q^β, neutron-star solutions that admit power-series expansions at the center or at infinity collapse to General Relativity; genuine beyond-GR effects must be non-analytic.

  2. Complete background cosmology of parity-even quadratic metric-affine gravity

    gr-qc 2024-12 conditional novelty 6.0 of 10

    The full background dynamics of parity-even quadratic metric-affine gravity in FLRW spacetimes are derived, including branches with spatial-curvature screening and analytic de Sitter-like solutions.

  3. Symmetric Teleparallel Connection and Spherical Solutions in Newer GR

    gr-qc 2024-12 conditional novelty 6.0 of 10

    The authors derive a unified spherical connection from the coincident gauge and present two new vacuum solution families in Newer GR, with no GR counterpart.

  4. Physical nonviability of $f(\mathbb{Q})$ in the scalar-tensor representation

    gr-qc 2026-06 unverdicted novelty 4.0 of 10

    The scalar-tensor representation of f(Q) gravity reproduces the known ghost/strong-coupling obstruction, so the pathology is not an artifact of the original variables.

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