A bigravity model from noncommutative geometry

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 $\mathrm{GL}(2,\mathbb{C})$ 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.

16 pages, v2 matches the published version

References in corpus (30)

• Loop Quantum Cosmology: A Status Report
• Bimetric Gravity from Ghost-free Massive Gravity
• A Gravity Theory on Noncommutative Spaces
• Ghost-free Massive Gravity with a General Reference Metric
• On Non-Linear Actions for Massive Gravity
• Noncommutative Geometry and Gravity
• Interacting Spin-2 Fields
• Cosmological Solutions in Bimetric Gravity and their Observational Tests
• Cosmology with a spin
• Twisting all the way: from Classical Mechanics to Quantum Fields
• Noncommutative D=4 gravity coupled to fermions
• On Partially Massless Bimetric Gravity
• SL(2,C) Gravity with Complex Vierbein and Its Noncommutative Extension
• No-Go Theorems for Unitary and Interacting Partially Massless Spin-Two Fields
• Vielbein to the Rescue?
• Noncommutative gravity coupled to fermions: second order expansion via Seiberg-Witten map
• Noncommutative gravity at second order via Seiberg-Witten map
• NC $SO(2,3{)}_{\star }$ gravity: noncommutativity as a source of curvature and torsion
• Canonical structure of Tetrad Bimetric Gravity
• Noncommutative Symmetries and Gravity
• Noncommutative SO(2,3) gauge theory and noncommutative gravity
• Gauge and global symmetries of the candidate partially massless bimetric gravity
• Pauli-Fierz mass term in modified Plebanski gravity
• Noncommutative gravity with self-dual variables
• On stability of Friedmann-Lemaître-Robertson-Walker solutions in doubled geometries
• Spectral interaction between universes
• On almost commutative Friedmann-Lemaître-Robertson-Walker geometries
• Bi-gravity with a single graviton
• Towards modified bimetric theories within non-product spectral geometry
• Spectral interactions between strings in the Higgs background