Probing secret interactions of eV-scale sterile neutrinos with the diffuse supernova neutrino background

While three flavors of "active" neutrinos are consistent with mixing angle results within error bars, there are anomalies may be hints of physics beyond the standard model that can accommodate a fourth mostly "sterile" neutrino species with an eV-scale mass and a mixing angle with active neutrinos of order $\theta_0\simeq 0.1$. We describe a scenario with eV-scale sterile neutrinos that have self-interactions via a new gauge vector boson, a "secret" mediator $\phi$. We show that their production in the early Universe via mixing with active neutrinos is consistent with Big Bang Nucleosynthesis and free-streaming constraints in the Cosmic Microwave Background epoch. For $M_\phi=4-8$ keV and sterile neutrino coupling $g_s=10^{-4}$, we find that resonant interactions of diffuse supernova neutrinos with relic sterile neutrinos in transit to the Earth would cause spectral dips in the neutrino flux. We illustrate the corresponding (anti-)neutrino event distributions as a function of energy in the DUNE (Hyper-Kamiokande) detector.