Living with ghosts in Horava-Lifshitz gravity

TL;DR

This paper analyzes a specific branch of Horava-Lifshitz gravity with ghost instabilities, showing it can mimic dark matter and has a very low vacuum decay rate, but faces challenges due to strong coupling effects.

Contribution

It demonstrates that the projectable Horava-Lifshitz model can be consistent with observations and may serve as a dark matter candidate despite ghost issues.

Findings

Vacuum decay into photons is negligible across many parameters.

The strong coupling scale can be increased up to approximately 10 TeV.

At low momenta, the model resembles General Relativity with a dark matter-like fluid.

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.