Cosmological Origin for Cosmic Rays Above ${10}^{19}$ eV

The cosmic ray spectrum at ${10}^{19}\mathrm{e}\mathrm{V}-{10}^{20}\mathrm{e}\mathrm{V}$, reported by the Fly’s Eye and the AGASA experiments, is shown to be consistent with a cosmological distribution of sources of protons, with a power law generation spectrum $\mathrm{d}\ln N\mathrm{/}\mathrm{d}\ln E=-2.3\pm 0.5$ and energy production rate of $4.5\pm 1.5\times {10}^{44}\mathrm{e}\mathrm{r}\mathrm{g}{\mathrm{M}\mathrm{p}\mathrm{c}}^{-3}{\mathrm{y}\mathrm{r}}^{-1}$. The two events measured above ${10}^{20}\mathrm{e}\mathrm{V}$ are not inconsistent with this model. Verifying the existence of a ``black-body cutoff’', currently observed with low significance, would require $\sim 30$ observation-years with existing experiments, but only $\sim 1$ year with the proposed $\sim 5000{\mathrm{k}\mathrm{m}}^2$ detectors. For a cosmological source distribution, no anisotropy is expected in the angular distribution of events with energies up to $\sim5\times10^{19}{\rm eV}$.