A bigravity model from noncommutative geometry

TL;DR

This paper explores a noncommutative gravity model that extends general relativity with additional gravitational degrees of freedom, resembling bigravity, and analyzes its cosmological solutions and symmetries.

Contribution

It introduces a noncommutative gravity framework with a GL(2,C) gauge connection and two tetrads, revealing new interaction structures and cosmological dynamics.

Findings

Extra gravitational degrees of freedom persist in the commutative limit.

The effective action shows similarities with ghost-free bigravity.

Cosmological solutions exhibit two distinct dynamical branches.

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 extensions 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.