  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.
