Reducing cosmological small scale structure via a large dark
  matter-neutrino interaction: constraints and consequences
  Cold dark matter explains a wide range of data on cosmological scales.
However, there has been a steady accumulation of evidence for discrepancies
between simulations and observations at scales smaller than galaxy clusters.
Solutions to these small scale structure problems may indicate that simulations
need to improve how they include feedback from baryonic matter, or may imply
that dark matter properties differ from the standard cold, noninteracting
scenario. One promising way to affect structure formation on small scales is a
relatively strong coupling of dark matter to neutrinos. We construct an
experimentally viable, simple, renormalizable, model with new interactions
between neutrinos and dark matter. We show that addressing the small scale
structure problems requires dark matter with a mass that is tens of MeV, and a
present-day density determined by an initial particle-antiparticle asymmetry in
the dark sector. Generating a sufficiently large dark matter-neutrino coupling
requires a new heavy neutrino with a mass around 100 MeV. The heavy neutrino is
mostly sterile but has a substantial $\tau$ neutrino component, while the three
nearly massless neutrinos are partly sterile. We provide the first discussion
of how such dark matter-neutrino interactions affect neutrino (especially
$\tau$ neutrino) phenomenology. This model can be tested by future
astrophysical, particle physics, and neutrino oscillation data. A feature in
the neutrino energy spectrum and flavor content from a future nearby supernova
would provide strong evidence of neutrino-dark matter interactions. Promising
signatures include anomalous matter effects in neutrino oscillations due to
nonstandard interactions and a component of the $\tau$ neutrino with mass
around 100 MeV.
