IceCube PeV-EeV neutrinos and secret interactions of neutrinos

We show that the PeV neutrinos detected by IceCube put unique constraints on "secret" interactions of neutrinos with the cosmic neutrino background (CνB). The coupling must be g < 0.03 for the mediating boson mass mX ≲ 2MeV, g/m_X < 5 GeV^-1 for m_X ≳ 20MeV, and g/m_X < 0.07 GeV^-1 in between. We also investigate the possibility that neutrino cascades degrade highenergy neutrinos to PeV energies by upgrading CνB where the energy flux of PeV neutrinos can coincide with the Waxman-Bahcall bound or the cosmogenic neutrino flux for protons, thanks to energy conservation. However, a large coupling is required, which is disfavored by laboratory decay constraints. The suppression of PeV-EeV neutrinos is a testable prediction for the Askaryan Radio Array.