  We construct a model of dark energy with a technically natural small
contribution to cosmic acceleration, i.e. this contribution does not receive
corrections from other scales in the theory. The proposed acceleration
mechanism appears generically in the low-energy limit of gravity theories with
violation of Lorentz invariance that contain a derivatively coupled scalar
field Theta. The latter may be the Goldstone field of a broken global symmetry.
The model, that we call Theta-CDM, is a valid effective field theory up to a
high cutoff just a few orders of magnitude below the Planck scale. Furthermore,
it can be ultraviolet-completed in the context of Horava gravity. We discuss
the observational predictions of the model. Even in the absence of a
cosmological constant term, the expansion history of the Universe is
essentially indistinguishable from that of Lambda-CDM. The difference between
the two theories appears at the level of cosmological perturbations. We find
that in Theta-CDM the matter power spectrum is enhanced at subhorizon scales
compared to Lambda-CDM. This property can be used to discriminate the model
from Lambda-CDM with current cosmological data.
