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 -Minkowski spacetime in flat space in the presence of a Friedman-Lema\^{i}tre-Robertson-Walker (FLRW) cosmological background. We obtain a new expression for the variation of the speed of light, depending linearly on the ratio (photon energy / Lorentz violation scale), but also linearly on the cosmological time, the Hubble parameter and inversely proportional to the scale factor.
Cite
@article{arxiv.2009.01051,
title = {Dispersion Relations in $\kappa$-Noncommutative Cosmology},
author = {Paolo Aschieri and Andrzej Borowiec and Anna Pachoł},
journal= {arXiv preprint arXiv:2009.01051},
year = {2021}
}
Comments
20 pages. New version: 23 pages, added 4-dim. dispersion relations and numerical estimates