  Cosmic acceleration is widely believed to require either a source of negative
pressure (i.e., dark energy), or a modification of gravity, which necessarily
implies new degrees of freedom beyond those of Einstein gravity. In this paper
we present a third possibility, using only dark matter and ordinary matter. The
mechanism relies on the coupling between dark matter and ordinary matter
through an effective metric. Dark matter couples to an Einstein-frame metric,
and experiences a matter-dominated, decelerating cosmology up to the present
time. Ordinary matter couples to an effective metric that depends also on the
DM density, in such a way that it experiences late-time acceleration. Linear
density perturbations are stable and propagate with arbitrarily small sound
speed, at least in the case of `pressure' coupling. Assuming a simple
parametrization of the effective metric, we show that our model can
successfully match a set of basic cosmological observables, including
luminosity distance, BAO measurements, angular-diameter distance to last
scattering {\it etc.} For the growth history of density perturbations, we find
an intriguing connection between the growth factor and the Hubble constant. To
get a growth history similar to the $\Lambda$CDM prediction, our model predicts
a higher $H_0$, closer to the value preferred by direct estimates. On the flip
side, we tend to overpredict the growth of structures whenever $H_0$ is
comparable to the Planck preferred value. The model also tends to predict
larger redshift-space distortions at low redshift than $\Lambda$CDM.
