Dynamical dark energy and gravitational coupling from moving geometries

TL;DR

This paper introduces moving Cartan geometries with spacetime-dependent structure constants, leading to a gauge theory framework that naturally produces dynamical dark energy and gravitational coupling from geometric and matter fields.

Contribution

It develops a novel class of gauge actions based on moving geometries with variable structure constants, linking geometry to dark energy and gravity dynamics.

Findings

Derives equations of motion linking geometry and matter fields.

Shows the model predicts a dynamical dark energy component.

Demonstrates the action becomes topological asymptotically.

Abstract

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$\times$Weyl moving geometries. The actions feature a generalization of the Nieh-Yan topological term for a varying coupling constant. 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. The action becomes asymptotically topological when the gauge action contribution to dark energy vanishes.