Publications

Cartan geometry, characteristic classes, Lie algebroids: Applications to gravity and the BRST formalism

Jean Thibaut, PhD thesis, 2025

The first part of the thesis studies the formulation of gravitational gauge theories with local geometry described by Lie algebras with structure fields instead of structure constants and highlights applications to alleviate some of the tensions in cosmology and curvature singularity problems in gravitational theories. The second part of the thesis develops a unified framework based on broken splittings of Atiyah short exact sequences of Lie algebroids to describe both ordinary gauge theories with a Higgs sector and the BRST formalism. We finally adapt the results of the first part of the thesis to generalized gauge theories on Lie algebroids, thus providing a unified structure to describe these different applica- tions.

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Dynamical dark energy and gravitational coupling from moving geometries

Jean Thibaut, ArXiv preprint, 2025

We introduce the notion of moving Cartan geometries described by quotients of Lie groups and Lie algebras with spacetime dependant structure constants and construct associated deformed topological gauge action functionals for Lorentzian (including dS and AdS) and Lorentz*Weyl moving geometries. We compute the equations of motion of the gauge + matter actions and show that they dictate at each spacetime point the geometry, leading to both a dynamical source of dark energy and a dynamical gravitational coupling, described by combinations of scalars built from spacetime curvature, torsion and the matter content of the theory.

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Gravity as a deformed topological gauge theory

Jean Thibaut, Serge Lazzarini, Physical Review D (PRD), 2024

We describe a deformed topological gauge theory of gravity. The two examples studied are Lorentzian (including dS and AdS) and conformal geometry. We show the total gauge + matter action is perturbatively topological in the bare cosmological constant.

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