On the shape of the ultrahigh energy cosmic ray spectrum

We fit the ultrahigh energy cosmic ray spectra above ${10}^{19}\mathrm{eV}$ with different injection spectra at cosmic ray sources that are uniformly and homogeneously distributed in the Universe. We conclude that the current ultrahigh energy spectra are consistent with power laws of index $\alpha$ between 2.4 and 2.7. There is a slow dependence of these indices on the cosmological evolution of the cosmic ray sources, which in this model determines the end of the galactic cosmic rays spectrum.