Neutrino secret self-interactions: a booster shot for the cosmic neutrino background

Neutrinos might interact among themselves through forces that have so far remained hidden. Throughout the history of the Universe, such \emph{secret} interactions could lead to scatterings between the neutrinos from supernova explosions and the non-relativistic relic neutrinos left over from the Big Bang. Such scatterings can boost the cosmic neutrino background (C$\nu$B) to energies of ${\cal O}$(MeV), making it, in principle, observable in experiments searching for the diffuse supernova neutrino background. Assuming a model-independent, but flavor universal, four-Fermi interaction, we determine the upscattered cosmic neutrino flux, and derive constraints on such secret interactions from the latest results from Super-Kamiokande. Furthermore, we also study prospects for detection of the boosted flux in future lead-based coherent elastic neutrino-nucleus scattering experiments. Nevertheless, given current constraints on flavor universal self-interactions, we find that the upscattered C$\nu$B~contribution to the total DSNB flux is negligible, making a possible measurement of the boosted C$\nu$B insurmountable.