Testing Lorentz invariance of dark matter
  We study the possibility to constrain deviations from Lorentz invariance in
dark matter (DM) with cosmological observations. Breaking of Lorentz invariance
generically introduces new light gravitational degrees of freedom, which we
represent through a dynamical timelike vector field. If DM does not obey
Lorentz invariance, it couples to this vector field. We find that this coupling
affects the inertial mass of small DM halos which no longer satisfy the
equivalence principle. For large enough lumps of DM we identify a (chameleon)
mechanism that restores the inertial mass to its standard value. As a
consequence, the dynamics of gravitational clustering are modified. Two
prominent effects are a scale dependent enhancement in the growth of large
scale structure and a scale dependent bias between DM and baryon density
perturbations. The comparison with the measured linear matter power spectrum in
principle allows to bound the departure from Lorentz invariance of DM at the
per cent level.
