Emergence of Gravity's Dynamical and Topological Sectors from Pre-geometry
Abstract
We identify the complete set of fundamental building blocks for a 4D pre-geometric theory of gravity. Based on a gauge theory of SO(1,4) or SO(2,3) coupled to a Higgs-like field under the rigid constraint of general covariance in the unbroken phase, these building blocks - ℒMM, ℒW, ℒJ, ℒθ and ℒϑ - constitute the minimal generating set of independent field monomials from which any pre-geometric action, including arbitrary functionals thereof, can be constructed. While the most general pre-geometric theory can extend beyond linear combinations, these five irreducible invariants serve as the 'atomic' constituents of all possible pre-geometric dynamics. Upon spontaneous symmetry breaking, they collectively generate an emergent gravitational theory consisting of the Einstein-Hilbert action, the cosmological constant term and all 4D topological invariants: the Gauss-Bonnet, Pontryagin, Holst and Nieh-Yan terms. The unification of gravity's dynamical and topological sectors from a common pre-geometric source represents the central result of this work. We also uncover a see-saw mechanism linking the Planck mass and the cosmological constant, as well as several novel relations for the coupling constants of the topological sector, inclusive of the Barbero-Immirzi parameter. This framework establishes the pre-geometric foundations from which all aspects of gravitation can dynamically emerge, providing a unified starting point for quantum gravity, dark energy phenomenology and the study of topological phases in gravitational theories.
Versions
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BibTeX
@misc{addazi2026emergence,
title = {{Emergence of Gravity's Dynamical and Topological Sectors from Pre-geometry}},
author = {Andrea Addazi and Giuseppe Meluccio},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10619},
eprint = {2609.10619},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10619},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Emergence of Gravity's Dynamical and Topological Sectors from Pre-geometry
AU - Andrea Addazi
AU - Giuseppe Meluccio
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.10619
UR - https://arxiv.org/abs/2609.10619
AB - We identify the complete set of fundamental building blocks for a 4D pre-geometric theory of gravity. Based on a gauge theory of SO(1,4) or SO(2,3) coupled to a Higgs-like field under the rigid constraint of general covariance in the unbroken phase, these building blocks - ℒ_MM, ℒ_W, ℒ_J, ℒ_θ and ℒ_ϑ - constitute the minimal generating set of independent field monomials from which any pre-geometric action, including arbitrary functionals thereof, can be constructed. While the most general pre-geometric theory can extend beyond linear combinations, these five irreducible invariants serve as the 'atomic' constituents of all possible pre-geometric dynamics. Upon spontaneous symmetry breaking, they collectively generate an emergent gravitational theory consisting of the Einstein-Hilbert action, the cosmological constant term and all 4D topological invariants: the Gauss-Bonnet, Pontryagin, Holst and Nieh-Yan terms. The unification of gravity's dynamical and topological sectors from a common pre-geometric source represents the central result of this work. We also uncover a see-saw mechanism linking the Planck mass and the cosmological constant, as well as several novel relations for the coupling constants of the topological sector, inclusive of the Barbero-Immirzi parameter. This framework establishes the pre-geometric foundations from which all aspects of gravitation can dynamically emerge, providing a unified starting point for quantum gravity, dark energy phenomenology and the study of topological phases in gravitational theories.
ER -