  Do neutrinos have sizable self-interactions? They might. Laboratory
constraints are weak, so strong effects are possible in astrophysical
environments and the early universe. Observations with neutrino telescopes can
provide an independent probe of neutrino self ("secret") interactions, as the
sources are distant and the cosmic neutrino background intervenes. We define a
roadmap for making decisive progress on testing secret neutrino interactions
governed by a light mediator. This progress will be enabled by IceCube-Gen2
observations of high-energy astrophysical neutrinos. Critical to this is our
comprehensive treatment of the theory, taking into account previously neglected
or overly approximated effects, as well as including realistic detection
physics. We show that IceCube-Gen2 can realize the full potential of neutrino
astronomy for testing neutrino self-interactions, being sensitive to
cosmologically relevant interaction models. To facilitate forthcoming studies,
we release nuSIProp, a code that can also be used to study neutrino
self-interactions from a variety of sources.
