  High-energy neutrinos from astrophysical transients serve as a probe of
neutrino physics beyond the Standard Model. In particular, nonstandard
interaction of neutrinos with the cosmic neutrino background or dark matter
(DM) may have imprints on not only their spectra but also the arrival and
time-delay distributions. Assuming that the interaction occurs at most once
during the neutrino propagation, we provide general analytic formulas for light
curves of the neutrino echoes induced by BSM. The formulas can be used for
constraining neutrino-neutrino scattering, neutrino-DM scattering, and other
scattering processes experienced by relativistic particles.
