Living with ghosts in Hořava-Lifshitz gravity

Abstract: We consider the branch of the projectable Hořava-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 Λ ∼ 10 TeV. At lower momenta, the projectable Hořava-Lifshitz gravity is equivalent to General Relativity supplemented by a fluid with a small positive sound speed squared (10−42 ≲) cs2 ≲ 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 Hořava’s proposal on quantum gravity. Apart from the Hořava-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.