paper

Hořava Gravity at a Lifshitz Point: A Progress Report

arXiv:1701.06087 · doi:10.1142/S0218271817300142

Abstract

Hořava gravity at a Lifshitz point is a theory intended to quantize gravity by using techniques of traditional quantum field theories. To avoid Ostrogradsky's ghosts, a problem that has been plaguing quantization of general relativity since the middle of 1970's, Hořava chose to break the Lorentz invariance by a Lifshitz-type of anisotropic scaling between space and time at the ultra-high energy, while recovering (approximately) the invariance at low energies. With the stringent observational constraints and self-consistency, it turns out that this is not an easy task, and various modifications have been proposed, since the first incarnation of the theory in 2009. In this review, we shall provide a progress report on the recent developments of Hořava gravity. In particular, we first present four most-studied versions of Hořava gravity, by focusing first on their self-consistency and then their consistency with experiments, including the solar system tests and cosmological observations. Then, we provide a general review on the recent developments of the theory in three different but also related areas: (i) universal horizons, black holes and their thermodynamics; (ii) non-relativistic gauge/gravity duality; and (iii) quantization of the theory. The studies in these areas can be generalized to other gravitational theories with broken Lorentz invariance.

revtex4, three figures. Corrected various typos. Int. J. Mod. Phys. D26 (2017) 1730014

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