Secret interactions of eV-scale sterile neutrinos and the diffuse supernova neutrino background flux

For a sterile neutrino with an eV-scale mass and vacuum mixing angle of order $\theta_0\simeq 0.1$, our evaluation of big bang nucleosynthesis and cosmic microwave background constraints allow a new gauge sector for sterile neutrino ``secret interactions'' with a gauge boson mass between a few keV and $\sim 100$ keV and sterile gauge boson couplings of order $g_s\simeq 10^{-4}-10^{-2}$. Relic sterile neutrinos with $m_s=1$ eV that interact via gauge bosons with a mass between $5-8$ keV and couplings in this range would distort the spectrum of the diffuse supernova neutrino background flux. We explore the potential for the distortion to be measured at DUNE and Hyper-Kamiokande.