Neutrino refraction by the cosmic neutrino background

Abstract

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.

12 pages, v3: published version

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• Implications of $\text{SU}(2{)}_L$ gauge invariance for constraints on Lorentz violation
• Formal Developments for Lorentz-Violating Dirac Fermions and Neutrinos
• Neutrino induced vorticity, Alfven waves and the normal modes
• Constraining the isotropic CPT-odd coefficients of the Standard Model Extension by a combined DUNE and ESSnuSB analysis