Observations of cosmic rays with energies above \sim 4 x 1010{GeV} have inspired several speculative suggestions concerning their origin. The crucial question is whether or not the spectrum exhibits the expected `GZK cutoff' at this energy - concerning which there are presently contradictory results. If there is indeed a cutoff, then the sources are cosmologically distant and rather exotic in nature. If there is no cutoff then new physics is required.
PACS numbers: 96.40.Pq, 98.70.Sa, 95.30.Cq
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