Proposed astrophysical test of Lorentz invariance

Working in the context of a Lorentz-violating extension of the standard model we show that estimates of Lorentz symmetry violation extracted from ultra-high-energy cosmic rays beyond the Greisen-Kuzmin-Zatsepilk (GZK) cutoff allow for setting bounds on parameters of that extension. Furthermore, we argue that a correlated measurement of the difference in the arrival time of gamma-ray photons and neutrinos emitted from active galactic nuclei or gamma-ray bursts may provide a signature of possible violation of Lorentz symmetry. We have found that this time delay is energy independent; however it has a dependence on the chirality of the particles involved. We also briefly discuss the known settings where the mechanism for spontaneous violation of Lorentz symmetry in the context of string/M-theory may take place.