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The energy losses and spectra of Ultra High Energy Cosmic Rays (UHECR) are calculated for protons as primary particles. The attention is given to the energy losses due to electron-positron production in collisions with the microwave 2.73 K photons. The energy spectra are calculated for several models, which differ by production spectra and by source distribution, namely: (i) Uniform distribution of the sources with steep generation spectra with indices 2.4 - 2.7, with cosmological evolution and without it. In this case it is possible to fit the shape of the observed spectrum up to 8.10^{19} eV, but the required CR emissivity is too high and the GZK cutoff is present. (ii) Uniform distribution of the sources with flat generation spectrum dE/E^2 which is relevant to GRBs. The calculated spectrum is in disagreement with the observed one. The agreement at Elesssim 8.10^{19} eV can be reached using a complex generation spectrum, but the required CR emissivity is three orders of magnitude higher than that of GRBs, and the predicted spectrum has the GZK cutoff. (iii) The case of local enhancement within region of size 10 - 30 Mpc with overdensity given by factor 3- 30. The overdensity larger than 10 is needed to eliminate the GZK cutoff.
More than 100 years after the discovery of cosmic rays and various experimental efforts, the origin of ultra-high energy cosmic rays (E > 100 PeV) remains unclear. The understanding of production and propagation effects of these highest energetic par
We present a strong hint of a connection between high energy $gamma$-ray emitting blazars, very high energy neutrinos, and ultra high energy cosmic rays. We first identify potential hadronic sources by filtering $gamma$-ray emitters %from existing ca
The origin of the ultra high energy cosmic rays (UHECR) with energies above E > 1017eV, is still unknown. The discovery of their sources will reveal the engines of the most energetic astrophysical accelerators in the universe. This is a written versi
We explore the joint implications of ultrahigh energy cosmic ray (UHECR) source environments -- constrained by the spectrum and composition of UHECRs -- and the observed high energy astrophysical neutrino spectrum. Acceleration mechanisms producing p
The origin of ultra high energy cosmic rays promises to lead us to a deeper understanding of the structure of matter. This is possible through the study of particle collisions at center-of-mass energies in interactions far larger than anything possib