Do we observe ultra high energy cosmic rays above the Greisen - Zatsepin - Kuzmin cutoff due to violation of Lorentz invariance ?

Do we observe ultra high energy cosmic rays above the Greisen-Zatsepin-Kuzmin cutoff due to violation of Lorentz invariance? Abstract Violation of Lorentz invariance has been suggested by Coleman and Glashow as a possible explanation of observing ultra high energy cosmic ray events above the Greisen Zatsepin Kuzmin cutoff. Earlier some of the ultra high energy cosmic ray events have been correlated with quasars and BL Lac objects. Assuming that there is violation of Lorentz invariance, we calculate the neutron event rates for some of the EGRET sources (including γ-ray loud BL Lac objects) which can be correlated with ultrahigh energy cosmic ray events observed by AGASA above energy 4 × 10 19 eV. We look for the evidence of the scenario of violation of Lorentz invariance, but our comparison of the calculated event rates with the observational data from AGASA does not show any signature of that scenario. Observational data on ultra high energy cosmic ray events have been recorded by different experiments like Fly's Eye, Akeno Giant Air Shower Array (AGASA) , Yakutsk experiment, Haverah Park, Volcano Ranch experiment and Sydney University Giant Air-shower Recorder (SUGAR) [1, 7]. The composition of the ultra high energy cosmic rays (UHECR) has been studied in [8, 10]. Data from Fly's Eye experiment [8] suggest that the chemical composition is dominated by heavy nuclei up to ankle (10 18.5)eV and thereafter by lighter component like protons. The Agasa data [10] suggests a mixed composition of both protons and heavier nuclei. The present experiments do not give us enough information about the chemical composition of primary UHECR. This topic has been addressed in [11]. If the UHECR are nuclei, then what could be their origin and how they propagated in the extragalactic magnetic field are at present exciting fields of studies. References [12, 15] discuss different suggestions on these issues.