Abstract
If the most energetic cosmic rays that have been detected are of extragalactic origin, and their sources were strong radio emitters, the radio-astronomical evidence suggests that the output from such sources must have been very much greater in the past than at present, varying roughly as t−3 over a long period. In this case, the importance of interactions between the universal flux of microwaves and intergalactic cosmic-ray protons and nuclei above 1015 eV is greatly increased, because of "red shifts" in the energies of the nuclei and the microwaves, and changes in density. The probable result is shown to be a steepening in the proton energy spectrum from a slope of –1.5 to –2.2 over the range 1016 to 1018 eV, as is observed, if the energy spectrum at production is always simply E−1.5.This could mean that the "ankle" in the observed spectrum near 3 × 1018 eV is related to the interaction mentioned, and is not a transition from galactic to extragalactic rays.Difficulties remain in accounting for the spectrum above 3 × 1019 eV.

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