Abstract
We study noncommutative deformations of the waveequation in curved backgrounds and discuss the modification of thedispersion relations due to noncommutativity combined withcurvature of spacetime. Our noncommutative differential geometry approach is based on Drinfeld twistdeformation, and can be implemented for any twist and any curvedbackground. We discuss in detail the Jordanian twist — givingκ-Minkowski spacetime in flat space — in the presence of aFriedman-Lemaître-Robertson-Walker (FLRW) cosmological background.We obtain a new expression for the variation of the speed of light, depending linearly onthe ratio E ph/E LV (photon energy/Lorentz violation scale),but also linearly on the cosmological time, the Hubble parameter andinversely proportional to the scale factor.
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