  The neutrinos in the diffuse supernova neutrino background (DSNB) travel over
cosmological distances and this provides them with an excellent opportunity to
interact with dark relics. We show that a cosmologically-significant relic
population of keV-mass sterile neutrinos with strong self-interactions could
imprint their presence in the DSNB. The signatures of the self-interactions
would be ``dips" in the otherwise smooth DSNB spectrum. Upcoming large-scale
neutrino detectors, for example Hyper-Kamiokande, have a good chance of
detecting the DSNB and these dips. If no dips are detected, this method serves
as an independent constraint on the sterile neutrino self-interaction strength
and mixing with active neutrinos. We show that relic sterile neutrino
parameters that evade X-ray and structure bounds may nevertheless be testable
by future detectors like TRISTAN, but may also produce dips in the DSNB which
could be detectable. Such a detection would suggest the existence of a
cosmologically-significant, strongly self-interacting sterile neutrino
background, likely embedded in a richer dark sector.
