Ultrahigh-energy cosmic-ray spectrum

We analyze the evolution of the ultrahigh-energy cosmic-ray spectrum upon traversing the 2.7 °K microwave background with respect to pion photoproduction, pair-production reactions, and cosmological effects. Our approach employs exact transport equations which manifestly conserve nucleon number and embody the laboratory details of these reactions. A spectrum enhancement appears around 6×10¹⁹ eV due to the ‘‘pile-up’’ of energy-degraded nucleons, and a ‘‘dip’’ occurs around 10¹⁹ eV due to combined effects. Both of these features appear in the observational spectrum. We analyze the resulting neutrino spectrum and the effects of cosmological source distributions. We present a complete model of the ultrahigh-energy spectrum and anisotropy in reasonable agreement with observation and which predicts an observable electron-neutrino spectrum.