  The detection of the high-energy neutrino event, IceCube-170922A,
demonstrated that multimessenger particle astrophysics triggered by neutrino
alerts is feasible. We consider time delay signatures caused by secret neutrino
interactions with the cosmic neutrino background and dark matter and suggest
that these can be used as a novel probe of neutrino interactions beyond the
Standard Model (BSM). The tests with BSM-induced neutrino echoes are distinct
from existing constraints from the spectral modification and will be enabled by
multimessenger observations of bright neutrino transients with future
experiments such as IceCube-Gen2, KM3Net, and Hyper-Kamiokande. The constraints
are complementary to those from accelerator and laboratory experiments and
powerful for testing various particle models that explain tensions prevailing
in the cosmological data.
