Simulating neutrino echoes induced by secret neutrino interactions

New neutrino interactions beyond the Standard Model (BSM) have been of much interest in not only particle physics but also cosmology and astroparticle physics. We numerically investigate the time delay distribution of astrophysical neutrinos that interact with the cosmic neutrino background. Using the Monte Carlo method, we develop a framework that enables us to simulate the time-dependent energy spectra of high-energy neutrinos that experience even multiple scatterings en route and to handle the sharp increase in the cross section at the resonance energy. As an example, we focus on the case of secret neutrino interactions with a scalar mediator. While we find the excellent agreement between analytical and simulation results for small optical depths, our simulations enable us to study optically thick cases that are not described by the simplest analytic estimates. Our simulations are used to understand effects of cosmological redshifts, neutrino spectra and flavors. The developments will be useful for probing BSM neutrino interactions with not only current neutrino detectors such as IceCube and Super-Kamiokande but also future neutrino detectors such as IceCube-Gen2 and Hyper-Kamiokande.