Ultra High Energy Cosmic Rays in Our Universe

Our Universe is described jointly by Einstein's relativity principle and the quantum principle; there the existence of the smallest units of matter, such as electrons, neutrinos, quarks, and photons, is well established and the smallest units of matter are described by the Standard Model. Based on these, we have a clear picture for the propagation of ultra high energy cosmic rays (UHECR's), for energies greater than $E > 10^{13}\, eV$ but less than $E < 10^{26}\, eV$, in the cosmic medium of the Cosmic Microwave Background (CMB) and of the cosmic background neutrinos (CB$ν$'s). We find that the CMB plays a pivot role in this energy range, so that the observed "knee(s)" and the "ankle" could be understood in reasonable terms. What we might observe at the energy near $10^{25}\,eV$', the so-called "$W^\pm$ bursts" or "$Z^0$ bursts", is briefly discussed. Meanwhile, in the early Universe, the CB$ν$'s, in view of the tiny neutrino mass, gave rise to the clustering phenomenon, resulting in a neutrino halo attached to each visual ordinary-matter object, such as the Earth, the Sun, and stars - with the $PeV$ neutrinos near the surface of the Fermi-Dirac sphere of the neutrino halo of the Earth playing the most fundamental role.

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