On Big Bang Relics, the Neutrino Mass and the Spectrum of Cosmic Rays

It is shown that high-energy features of the cosmic ray spectrum, in particular the kink around 4 PeV and the corresponding change in spectral index, may be explained from interactions between highly energetic cosmic protons and relic Big Bang antineutrinos, if the latter have a rest mass of about 0.4 eV/$c^2$. This explanation is supported by experimental data from extensive air-shower experiments, and in particular by the observation (Fly's Eye) of a second kink around 300 PeV, and by the abrupt change in the chemical composition of the cosmic ray spectrum that occurs at that energy. Both facts follow naturally from our theory, which predicts additional verifiable features of the cosmic ray spectrum in the few-PeV region, e.g. an abrupt decrease in the $p/\alpha$ ratio.