Living with ghosts in Horava-Lifshitz gravity

We consider the branch of the projectable Hofava-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 similar to 10 TeV. At lower momenta, the projectable Hofava-Lifshitz gravity is equivalent to General Relativity supplemented by a fluid with a small positive sound speed squared (10(-42) less than or similar to) c(s)(2) less than or similar to 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 Hofava's proposal on quantum gravity. Apart from the Hofava-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.