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Cold dark matter explains a wide range of data on cosmological scales.However, there has been a steady accumulation of evidence for discrepanciesbetween simulations and observations at scales smaller than galaxy clusters.Solutions to these small scale structure problems may indicate that simulationsneed to improve how they include feedback from baryonic matter, or may implythat dark matter properties differ from the standard cold, noninteractingscenario. One promising way to affect structure formation on small scales is arelatively strong coupling of dark matter to neutrinos. We construct anexperimentally viable, simple, renormalizable, model with new interactionsbetween neutrinos and dark matter. We show that addressing the small scalestructure problems requires dark matter with a mass that is tens of MeV, and apresent-day density determined by an initial particle-antiparticle asymmetry inthe dark sector. Generating a sufficiently large dark matter-neutrino couplingrequires a new heavy neutrino with a mass around 100 MeV. The heavy neutrino ismostly sterile but has a substantial $\tau$ neutrino component, while the threenearly massless neutrinos are partly sterile. We provide the first discussionof how such dark matter-neutrino interactions affect neutrino (especially$\tau$ neutrino) phenomenology. This model can be tested by futureastrophysical, particle physics, and neutrino oscillation data. A feature inthe neutrino energy spectrum and flavor content from a future nearby supernovawould provide strong evidence of neutrino-dark matter interactions. Promisingsignatures include anomalous matter effects in neutrino oscillations due tononstandard interactions and a component of the $\tau$ neutrino with massaround 100 MeV.

Reducing cosmological small scale structure via a large dark matter-neutrino interaction: constraints and consequences