  We investigate the cosmological effects of a neutrino interaction with cold
dark matter. We postulate a neutrino that interacts with a ``neutrino
interacting dark matter'' (NIDM) particle with an elastic-scattering cross
section that either decreases with temperature as $T^2$ or remains constant
with temperature. The neutrino--dark-matter interaction results in a
neutrino--dark-matter fluid with pressure, and this pressure results in
diffusion-damped oscillations in the matter power spectrum, analogous to the
acoustic oscillations in the baryon-photon fluid. We discuss the bounds from
the Sloan Digital Sky Survey on the NIDM opacity (ratio of cross section to
NIDM-particle mass) and compare with the constraint from observation of
neutrinos from supernova 1987A. If only a fraction of the dark matter interacts
with neutrinos, then NIDM oscillations may affect current cosmological
constraints from measurements of galaxy clustering. We discuss how detection of
NIDM oscillations would suggest a particle-antiparticle asymmetry in the
dark-matter sector.
