  If all or a fraction of the dark matter (DM) were coupled to a bath of dark
radiation (DR) in the early Universe we expect the combined DM-DR system to
give rise to acoustic oscillations of the dark matter until it decouples from
the DR. Much like the standard baryon acoustic oscillations, these dark
acoustic oscillations (DAO) imprint a characteristic scale, the sound horizon
of dark matter, on the matter power spectrum. We compute in detail how the
microphysics of the DM-DR interaction affects the clustering of matter in the
Universe and show that the DAO physics also gives rise to unique signatures in
the temperature and polarization spectra of the cosmic microwave background
(CMB). We use cosmological data from the CMB, baryon acoustic oscillations
(BAO), and large-scale structure to constrain the possible fraction of
interacting DM as well as the strength of its interaction with DR. Like nearly
all knowledge we have gleaned about dark matter since inferring its existence
this constraint rests on the betrayal by gravity of the location of otherwise
invisible dark matter. Although our results can be straightforwardly applied to
a broad class of models that couple dark matter particles to various light
relativistic species, in order to make quantitative predictions, we model the
interacting component as dark atoms coupled to a bath of dark photons. We find
that linear cosmological data and CMB lensing put strong constraints on
existence of DAO features in the CMB and the large-scale structure of the
Universe. Interestingly, we find that at most ~5% of all DM can be very
strongly interacting with DR. We show that our results are surprisingly
constraining for the recently proposed Double-disk DM model, a novel example of
how large-scale precision cosmological data can be used to constrain galactic
physics and sub-galactic structure.
