Features of the spectrum of the most energetic cosmic-ray protons produced by their passage through the 2.7 K universal background radiation are investigated by Monte Carlo techniques. We discuss the influence of various factors on the spectrum of protons observed at Earth with energies above 3×${10}^{19}$ eV. These factors include the shape of the initial cosmic-ray spectrum, the spatial distribution of sources, and the energy-dependent diffusion and escape of particles from a confinement region.

• Received 7 March 1994

DOI:https://doi.org/10.1103/PhysRevD.50.1892