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The only invariant speed in special relativity is c; therefore, if someneutrinos travel at even tiny speeds above c, normal special relativity isincomplete and any superluminal speed may be possible. I derive a limit onsuperluminal neutrino speeds v >> c at high energies by noting that such speedswould increase the size of the neutrino horizon. The increased volume of theUniverse visible leads to a brighter astrophysical neutrino background. Thenondetection of "guaranteed" neutrino backgrounds from star-forming galaxiesand ultrahigh energy cosmic rays (UHECRs) constrains v/c at TeV--ZeV energies.I find that v/c <= 820 at 60 TeV from the nondetection of neutrinos fromstar-forming galaxies. The nondetection of neutrinos from UHECRs constrains v/cto be less than 2500 at 0.1 EeV in a pessimistic model and less than 4.6 at 4EeV in an optimistic model. The UHECR neutrino background nondetection isstrongly inconsistent with a naive quadratic extrapolation of the OPERA resultsto EeV energies. The limits apply subject to some caveats, particularly thatthe expected pionic neutrino backgrounds exist and that neutrinos travel fasterthan c when they pass the detector. They could be improved substantially as theexpected neutrino backgrounds are better understood and with new experimentalneutrino background limits. I also point out that extremely subluminal speedswould result in a much smaller neutrino background intensity than expected.

Olber's Paradox for Superluminal Neutrinos: Constraining Extreme Neutrino Speeds at TeV-ZeV Energies with the Diffuse Neutrino Background