  We have determined the dispersion relation of a neutrino test particle
propagating in the cosmic neutrino background. Describing the relic neutrinos
and antineutrinos from the hot big bang as a dense medium, a matter potential
or refractive index is obtained. The vacuum neutrino mixing angles are
unchanged, but the energy of each mass state is modified. Using a matrix in the
space of neutrino species, the induced potential is decomposed into a part
which produces signatures in beta-decay experiments and another part which
modifies neutrino oscillations. The low temperature of the relic neutrinos
makes a direct detection extremely challenging. From a different point of view,
the identified refractive effects of the cosmic neutrino background constitute
an ultralow background for future experimental studies of nonvanishing Lorentz
violation in the neutrino sector.
