On the Propagation of Extragalactic High Energy Cosmic and Gamma-Rays

The origin and nature of ultrahigh energy cosmic rays with energies above $10^{20}\,$eV is a puzzle for the physics and astrophysics of cosmic rays which is still unresolved. In this paper, I report on an extensive study on the propagation of extragalactic nucleons, $\gamma$-rays, and electrons in the energy range between $10^8\,$eV and $10^{23}\,$eV. I have devised an efficient numerical method to solve the transport equations for cosmic ray spectral evolution. The universal radiation background spectrum in the energy range between $\simeq 10^{9}\,$eV and $\simeq 1\,$eV is considered in the numerical code, including the diffuse radio background, the cosmic microwave background, and the infrared/optical background, as well as a possible extragalactic magnetic field. I apply the code to compute the particle spectra predicted by various models of ultrahigh energy cosmic ray origin. A comparison with the observed fluxes, especially the diffuse $\gamma$-ray background in several energy ranges, allows one to constrain certain classes of models. I conclude that scenarios which attribute the highest energy cosmic rays to Grand Unification Scale physics or to cosmological Gamma Ray Bursts are viable at the present time.