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The cosmic-ray spectra measured by the Fly's Eye (red), HiRes (cyan) and Yakutsk (green) experiments compared with a model (orange line) in which cosmologically distant gamma-ray bursts generate cosmic rays according to the relation (dN/dE) is proportional to E-2, where N is the number of particles and E is the energy.
The contribution by galactic cosmic rays, which are assumed to extend to high energies such that dN/dE is proportional to E-3.5, is shown by the blue line. The purple line is a naive extrapolation of the spectrum between 1010 and 5 x 1010 GeV beyond the GZK energy.