Hypercomplex General Relativity (HGR): A Symplectic and Weyl-Geometric Reformulation with Late-Time Cosmological Applications
Authors/Creators
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1.
Institut National de la Recherche Agronomique
Description
This deposit gathers and documents the complete body of work related to Hypercomplex General Relativity (HGR), an extension of General Relativity developed by Laurent Besson.
HGR introduces an internal hypercomplex structure within the spacetime metric, allowing a reformulation of gravity that preserves local consistency and the standard relativistic limit while avoiding Ostrogradsky-type instabilities.
The present record synthesizes successive versions of the model, including the initial formulation (2015), a comprehensive theoretical update (2025), and recent additions addressing critical discussions.
In a cosmological context, the model leads to a holographic-like behavior characterized by a late-time geometric component compatible with current observational constraints from the Cosmic Microwave Background and large-scale structure data.
This deposit includes the Lagrangian formulation, the field equations, and numerical implementations based on a modified version of standard cosmology codes, and is released within an open science framework to ensure long-term accessibility, reproducibility, and citation.
Keywords: general relativity, modified gravity, hypercomplex geometry, cosmology, theoretical physics.
Abstract (En)
This manuscript presents a geometric reformulation of General Relativity based on the introduction of hypercomplex structures and their expression within a symplectic framework.
The construction preserves local relativistic consistency and the standard General Relativity limit, while reorganizing the gravitational degrees of freedom such that the resulting Lagrangian involves at most second-order derivatives or degenerate higher-order combinations. As a consequence, the theory remains free of Ostrogradsky-type instabilities at the classical level.
The formalism is developed on a fibered geometric structure combining hypercomplex internal degrees of freedom, symplectic geometry, and Weyl-conformal compatibility. The associated Lagrangian, field equations, and curvature decompositions are derived explicitly, and their interpretation is discussed in both covariant and Hamiltonian terms.
Cosmological solutions are examined in homogeneous and isotropic settings, leading to modified late-time dynamics while preserving consistency with standard relativistic cosmology. A numerical implementation based on a modified cosmological solver is outlined to illustrate the phenomenological implications of the model.
This work is presented as an open theoretical preprint intended for scientific discussion and further investigation
Files
RGH_symplectique_complet_et_annexe_quantized.pdf
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Additional details
Additional titles
- Alternative title (French)
- Relativité Générale Hypercomplexe (RGH) : Reformulation symplectique et géométrie de Weyl avec applications cosmologiques tardives
Software
- Repository URL
- https://monblog.system-linux.fr/RGH-with-grok/
- Programming language
- Python
- Development Status
- Active