Relating Noncommutative SO(2,3) Gravity to the Lorentz-Violating Standard-Model Extension

Abstract

We consider a model of noncommutative gravity that is based on a spacetime with broken local SO(2,3) symmetry. We show that the torsion-free version of this model is contained within the framework of the Lorentz-violating Standard-Model Extension. We analyze in detail the relation between the torsion-free, quadratic limits of the broken SO(2,3) model and the Standard-Model Extension. As part of the analysis,we construct the relevant geometric quantities to quadratic order in the metric perturbation around a flat background.

10 pages, accepted in Symmetry

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Cited by in corpus (10)

• Backgrounds in gravitational effective field theory
• Signals for Lorentz violation in gravitational waves
• Measuring the stability of fundamental constants with a network of clocks
• 3+1 Formulation of the Standard-Model Extension Gravity Sector
• Hubble tension as a guide for refining the early Universe: Cosmologies with explicit local Lorentz and diffeomorphism violation
• Hamiltonian formulation of an effective modified gravity with nondynamical background fields
• Lorentz Violation and Sagnac Gyroscopes
• Construction of higher-order metric fluctuation terms in spacetime symmetry-breaking effective field theory
• Noncommutative $SO(2,3{)}_{\star }$ Gauge Theory of Gravity
• Cosmology in the presence of diffeomorphism-violating, nondynamical background fields