http://arxiv.org/abs/1701.06087
Ho\v{r}ava’s quantum gravity at a Lifshitz point is a theory intended to quantize gravity by using traditional quantum field theories. To avoid Ostrogradsky’s ghosts, a problem that has been facing in quantization of general relativity since the middle of 1970’s, Ho\v{r}ava 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 development of Ho\v{r}ava gravity. In particular, we first present four so far most-studied versions of Ho\v{r}ava 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 development 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 easily generalized to other gravitational theories with broken Lorentz invariance.
A. Wang
Tue, 24 Jan 17
12/63
Comments: revtex4, three figures. To be submitted to Int. J. Mod. Phys. D
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