Abstract
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.
Highlights
Violation of Lorentz invariance at the high energies may have dramatic consequences in a view of another long-standing problem — the renormalization of gravity
The projectable Horava-Lifshitz gravity is equivalent to General Relativity supplemented by a fluid with a small positive sound speed squared (10−42 ) c2s 10−20, that could be a promising candidate for the Dark Matter
We showed that the strong coupling scale of the projectable HoravaLifshitz gravity can be raised to 10 TeV, upon switching to the ghost unstable branch of the scenario
Summary
We start with a brief review of the Horava-Lifshitz gravity theory, focusing on its projectable version. It is interesting to note that the action (2.10) by itself is not specific to the projectable Horava-Lifshitz gravity, but may arise in a drastically different framework In this regard, the mimetic matter scenario has brought some attention recently [36]. In the mimetic matter case, the higher derivative term as in eq (2.10) is added in view of some phenomenological goals [37,38,39], i.e., it does not follow immediately from the first principles underlying the scenario Keeping in mind this potentially interesting scenario, we proceed with the HoravaLifshitz model as the main focus of the present work. The action (2.10) will be the starting point of our further discussions
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