Two of the key unresolved issues facing Standard Model physics are (i) the appearance of a small but non-zero neutrino mass, and, (ii) the missing mass problem in the Universe. The focus of this paper is a previously proposed low energy effective theory that couples a dark scalar to Standard Model neutrinos. This provides a stable dark matter candidate as well as radiatively generating a neutrino mass. Within this framework we will then construct an entirely new bound from the IceCube-170922A event which takes into account (i) the possible neutrino mass hierarchies, (ii) the effect of cosmological redshift on e.g. the number density of cosmic neutrino background neutrinos, and, (iii) the non-degeneracy of neutrino mass and flavour eigenstates. This builds on work by Kelly and Machado (2018), where the authors placed new constraints on neutrinophilic and axion dark matter models. At low mediator masses, we find an improvement of an order of magnitude on current constraints from kaon decays. The constraint is complimentary (and slightly weaker) than current constraints from Big Bang Nucleosynthesis and the Cosmic Microwave Background. We explore how future higher energy events could improve this bound.
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