The extra high energy cosmic rays spectrum in view of the decay of proton into Planck neutrinos

Abstract

It is assumed that proton decays into Planck neutrinos. The energy of the Planck neutrino is equal to the Planck mass in the preferred rest frame. In the frame moving relative to the preferred rest frame the energy of the Planck neutrino reduces by the corresponding Lorentz factor. The lifetime of proton depends on the kinetic energy of proton relative to the preferred rest frame. The time required for proton travel from the source to the earth defines the limiting energy. Protons with the energies more than the limiting energy decay and do not give contribution in the EHECRs spectrum. It is shown that EHECRs with the energies $E>3 \times 10^{18} {\rm eV}$ can be identified with the Planck neutrinos.