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تسجيل مستخدم جديدDispersion Relations in $kappa$-Noncommutative Cosmology
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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-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 $E_{ph}/E_{LV}$ (photon energy / Lorentz violation scale), but also linearly on the cosmological time, the Hubble parameter and inversely proportional to the scale factor.
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Lectures by the author at the 1986 Cargese summer school modestly corrected and uploaded for greater accessibility. Some of the authors views on the quantum mechanics of cosmology have changed from those presented here but may still be of historical
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