  The role of Lorentz invariance as a fundamental symmetry of nature has been
lately reconsidered in different approaches to quantum gravity. It is thus
natural to study whether other puzzles of physics may be solved within these
proposals. This may be the case for the cosmological constant problem. Indeed,
it has been shown that breaking Lorentz invariance provides Lagrangians that
can drive the current acceleration of the universe without experiencing large
corrections from ultraviolet physics. In this work, we focus on the simplest
model of this type, called ThetaCDM, and study its cosmological implications in
detail. At the background level, this model cannot be distinguished from
LambdaCDM. The differences appear at the level of perturbations. We show that
in ThetaCDM, the spectrum of CMB anisotropies and matter fluctuations may be
affected by a rescaling of the gravitational constant in the Poisson equation,
by the presence of extra contributions to the anisotropic stress, and finally
by the existence of extra clustering degrees of freedom. To explore these
modifications accurately, we modify the Boltzmann code CLASS. We then use the
parameter inference code Monte Python to confront ThetaCDM with data from
WMAP-7, SPT and WiggleZ. We obtain strong bounds on the parameters accounting
for deviations from LambdaCDM. In particular, we find that the discrepancy
between the gravitational constants appearing in the Poisson and Friedmann
equations is constrained at the level 1.8%.
