Propagation of extragalactic high energy cosmic and γ rays

The observation of air showers from elementary particles with energies exceeding 10^20eV poses a puzzle to the physics and astrophysics of cosmic rays which is still unresolved. Explaining the origin and nature of these particles is a challenge. In order to constrain production mechanisms and sites, one has to account for the processing of particle spectra by interactions with radiation backgrounds and magnetic fields on the way to the observer. In this paper, I report on an extensive study on the propagation of extragalactic nucleons, -rays, and electrons in the energy range between 10^8eV and 10^25eV. We 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 10^-9eV and 10eV 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. We apply the code to compute the particle spectra predicted by several models of ultrahigh energy cosmic ray origin. A comparison with the observed fluxes, especially the diffuse -ray background in several energy ranges, allows one to constrain certain classes of models.