Ultra high energy cosmic rays: energy losses and spectra

The energy losses and spectra of Ultra High Energy Cosmic Rays (UHECR) are calculated for protons as the primary particles. An 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 indicies 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 · 1019 eV ; (ii) Uniform distribution of the sources with flat generation spectrum dE/E2 . This case is relevant to GRBs and results are in disagreement with observed spectrum. (iii) The case of local enhancement within region of size 10 30 Mpc with overdensity given by factor 3 100. The overdensity larger than 30 is needed to eliminate GZK cutoff.