Cosmic neutrino cascades from secret neutrino interactions

The first detection of high-energy astrophysical neutrinos by IceCube provides new opportunities for tests of neutrino properties. The long baseline through the cosmic neutrino background (C nu B) is particularly useful for directly testing secret neutrino interactions (nu SI) that would cause neutrino-neutrino elastic scattering at a larger rate than the usual weak interactions. We show that IceCube can provide competitive sensitivity to nu SI compared to other astrophysical and cosmological probes, which are complementary to laboratory tests. We study the spectral distortions caused by nu SI with a large s-channel contribution, which can lead to a dip, bump, or cutoff on an initially smooth spectrum. Consequently, nu SI may be an exotic solution for features seen in the IceCube energy spectrum. More conservatively, IceCube neutrino data could be used to set model-independent limits on nu SI. Our phenomenological estimates provide guidance for more detailed calculations, comparisons to data, and model building.