Do neutrinos have sizable self-interactions? This fundamental question, whose answer directly affects future precise astrophysical and cosmological observations, is difficult to directly test in the laboratory. For the last years, neutrino telescopes have been identified as unique tools to explore neutrino self-interactions. The actual discovery of astrophysical neutrinos and the advent of future neutrino telescopes, together with a more precise understanding of neutrino masses from laboratory and cosmological probes, calls for a robust theoretical description of the underlying particle physics and its connections with other neutrino observables. In this work, we set up such theoretical framework for present and future studies. We quantify the relevance of previously ignored effects, and we clarify the interplay with other experimental probes of neutrino properties. These directly affect the interpretation of present data in terms of self-interactions, as well as the testability of current "hints" in future facilities. After applying our formalism, we find that current IceCube data shows no evidence of neutrino self-interactions, and it is beginning to exclude self-interactions that have been argued to affect cosmological parameter extraction (most notably $H_0$). Furthermore, our results show that the future IceCube Gen2 observatory should be sensitive to many cosmologically relevant neutrino self-interaction models.
|Reference to paper (DOI or arXiv)||Work in progress|