Dispersion Relations in $\kappa$-Noncommutative Cosmology

Abstract

We study noncommutative deformations of the wave equation in curved backgrounds and discuss the modification of the dispersion relations due to noncommutativity combined with curvature of spacetime. Our noncommutative differential geometry approach is based on Drinfeld twist deformation, and can be implemented for any twist and any curved background. We discuss in detail the Jordanian twist $-$giving $\kappa$-Minkowski spacetime in flat space$-$ in the presence of a Friedman-Lemaître-Robertson-Walker (FLRW) cosmological background. We obtain a new expression for the variation of the speed of light, depending linearly on the ratio $E_{ph}/E_{LV}$ (photon energy / Lorentz violation scale), but also linearly on the cosmological time, the Hubble parameter and inversely proportional to the scale factor.

20 pages. New version: 23 pages, added 4-dim. dispersion relations and numerical estimates

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Cited by in corpus (5)

• Gauge theories on quantum spaces
• Noncommutative Yang model and its generalizations
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Lie-Poisson gauge theories and $\kappa$-Minkowski electrodynamics
• Newtonian cosmology and Evolution of kappa-deformed universe