  The cosmic neutrino background is both a dramatic prediction of the hot Big
Bang and a compelling target for current and future observations. The impact of
relativistic neutrinos in the early universe has been observed at high
significance in a number of cosmological probes. In addition, the non-zero mass
of neutrinos alters the growth of structure at late times, and this signature
is a target for a number of upcoming surveys. These measurements are sensitive
to the physics of the neutrino and could be used to probe physics beyond the
standard model in the neutrino sector. We explore an intriguing possibility
where light right-handed neutrinos are coupled to all, or a fraction of, the
dark matter through a mediator. In a wide range of parameter space, this
interaction only becomes important at late times and is uniquely probed by
late-time cosmological observables. Due to this coupling, the dark matter and
neutrinos behave as a single fluid with a non-trivial sound speed, leading to a
suppression of power on small scales. In current and near-term cosmological
surveys, this signature is equivalent to an increase in the sum of the neutrino
masses. Given current limits, we show that at most 0.5% of the dark matter
could be coupled to neutrinos in this way.
