Living with ghosts in Horava-Lifshitz gravity
  We consider the branch of the projectable Horava-Lifshitz model which
exhibits ghost instabilities in the low energy limit. It turns out that, due to
the Lorentz violating structure of the model and to the presence of a finite
strong coupling scale, the vacuum decay rate into photons is tiny in a wide
range of phenomenologically acceptable parameters. The strong coupling scale,
understood as a cutoff on ghosts' spatial momenta, can be raised up to $\Lambda
\sim 10$ TeV. At lower momenta, the projectable Horava-Lifshitz gravity is
equivalent to General Relativity supplemented by a fluid with a small positive
sound speed squared ($10^{-42}\lesssim$) $c^2_s \lesssim 10^{-20}$, that could
be a promising candidate for the Dark Matter. Despite these advantages, the
unavoidable presence of the strong coupling obscures the implementation of the
original Horava's proposal on quantum gravity. Apart from the Horava-Lifshitz
model, conclusions of the present work hold also for the mimetic matter
scenario, where the analogue of the projectability condition is achieved by a
non-invertible conformal transformation of the metric.
