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.