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. 
Sangjin Lee (The University of Chicago)