A bigravity model from noncommutative geometry
Marco de Cesare, Mairi Sakellariadou, Araceli Soler Oficial
TL;DR
The paper studies a twist-deformed noncommutative gravity model that yields a bigravity-like theory in the commutative limit, featuring a GL(2,C) gauge connection and two tetrads coupled via carefully structured interactions. It reveals an enhanced gauge symmetry and a rich cosmological structure, with Branch I displaying no propagating physical degrees of freedom in the reduced cosmological sector due to four first-class and two second-class constraints. Branch II allows arbitrary evolution of the scale factors on a fixed circle with purely spatial, generally nonzero torsion, reducing to de Sitter only under special tuning. The work highlights the potential generality of bigravity emergence in first-order formulations of noncommutative gravity and outlines future directions to explore perturbations, matter couplings, and connections to partially massless theories.
Abstract
Noncommutative gravity, based on a twist-deformation of the differential geometry of spacetime and a first-order formulation of the dynamics, requires additional gravitational degrees of freedom as well as an enlargement of the gauge group of Lorentz transformations of the tetrad frame. As such, it offers a theoretical playground to build fundamentally motivated extension to general relativity. The dynamical degrees of freedom include a ${\rm GL}(2,\mathbb{C})$ gauge connection and two independent tetrads. The theory allows for interaction terms between the two tetrads, whose structure displays some similarities with ghost-free bigravity. The extra gravitational degrees of freedom survive in the commutative limit. We show the effective action obtained in this limit, discuss its symmetries, and compare it with other bigravity theories. The dynamics of homogeneous and isotropic cosmological solutions split into two branches. One is characterized by a constant and purely spatial curvature two-form. The other displays a richer gauge freedom, and the Hamiltonian analysis of the dynamics reveals three extra first-class constraints in addition to the generator of time reparametrizations.