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 κ-Minkowski spacetime in flat space — in the presence of a Friedman-Lematre-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.

我们研究了弯曲背景下波动方程的非对易变形，并讨论了由于非对易性与时空曲率相结合对色散关系的修正。我们的非对易微分几何方法基于 Drinfeld 扭曲变形，并且可以用于任何扭曲和任何弯曲的背景。在弗里德曼-勒马特-罗伯逊-沃克 (FLRW) 宇宙学背景存在的情况下，我们详细讨论了约旦扭曲——在平面空间中给出 κ-闵可夫斯基时空。我们获得了光速变化的新表达式，线性取决于比率E _ph / E _LV（光子能量/洛伦兹破坏尺度），而且与宇宙时间呈线性关系，哈勃参数与尺度因子成反比。