The Pre-geometric Origin of Geometric Trinity of Gravity
Abstract
The so-called Geometric Trinity of Gravity is based on three distinct geometric features of spacetime, i.e.\ curvature, torsion and non-metricity, which give rise to equivalent dynamics for General Relativity (GR), Teleparallel Equivalent of General Relativity (TEGR) and Symmetric Teleparallel Equivalent of General Relativity (STEGR). Pre-geometric gravity, on the other hand, offers a unifying framework from which all metric-affine theories can emerge. Starting from a gauge formulation \textit{à la} Yang--Mills with a Higgs-like field, a mechanism of spontaneous symmetry breaking can give rise to an effective metric as well as to the classical dynamics of the gravitational field. In particular, the emergence of gravity in the spontaneously broken phase is shown to be consistent with all the different formulations of the Geometric Trinity of Gravity, in terms both of actions and of gauge choices for the affine connection. This general result is achieved by deriving and analysing suitable expressions in the unbroken phase for pre-geometric actions and for pre-geometric gauge-fixing conditions respectively.
Versions
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BibTeX
@misc{capozziello2026pregeometric,
title = {{The Pre-geometric Origin of Geometric Trinity of Gravity}},
author = {Salvatore Capozziello and Giuseppe Meluccio},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.17580},
eprint = {2606.17580},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.17580},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Pre-geometric Origin of Geometric Trinity of Gravity
AU - Salvatore Capozziello
AU - Giuseppe Meluccio
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2606.17580
UR - https://arxiv.org/abs/2606.17580
AB - The so-called Geometric Trinity of Gravity is based on three distinct geometric features of spacetime, i.e.\ curvature, torsion and non-metricity, which give rise to equivalent dynamics for General Relativity (GR), Teleparallel Equivalent of General Relativity (TEGR) and Symmetric Teleparallel Equivalent of General Relativity (STEGR). Pre-geometric gravity, on the other hand, offers a unifying framework from which all metric-affine theories can emerge. Starting from a gauge formulation \textit{à la} Yang--Mills with a Higgs-like field, a mechanism of spontaneous symmetry breaking can give rise to an effective metric as well as to the classical dynamics of the gravitational field. In particular, the emergence of gravity in the spontaneously broken phase is shown to be consistent with all the different formulations of the Geometric Trinity of Gravity, in terms both of actions and of gauge choices for the affine connection. This general result is achieved by deriving and analysing suitable expressions in the unbroken phase for pre-geometric actions and for pre-geometric gauge-fixing conditions respectively.
ER -