Time Delay in $\kappa$-Anti-de Sitter Spacetime

Abstract

Based on deformed translations in the $\kappa$-anti-de Sitter algebra, we derive a delay in the time of detection between a soft and a hard photon, which are simultaneously emitted at a distant event, to first order in the quantum gravity parameter. In the basis analyzed, the trajectories are undeformed, and the effect depends exclusively on the symmetry properties of the quantum algebra. The time delay depends linearly on the energy of the hard particle and has a sinusoidal dependence on the redshift of the source.

Title modified. Corrections on the translation parameters were made. 7 pages, 2 figures. Version published in PLB

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