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Ho\v{r}ava 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…
We argue that the true nature of the renormalizability of Horava-Lifshitz gravity lies in the presence of higher order spatial derivatives and not in the anisotropic Lifshitz scaling of space and time. We discuss the possibility of…
We study a version of the recently proposed modified $F(R)$ Ho\v{r}ava-Lifshitz gravity that abandons the projectability condition of the lapse variable. We discovered that the projectable version of this theory has a consistent Hamiltonian…
Horava gravity has been proposed as a renormalizable quantum gravity without the ghost problem through anisotropic scaling dimensions which break Lorentz symmetry in UV. In the Hamiltonian formalism, due to the Lorentz-violating terms, the…
In this paper we seek static spherically symmetric solutions of Horava-Lifshitz-like gravity with projectability condition. We consider the most general form of gravity action without detailed balance, and require the spacetime metric to…
[Abridged] In its standard formulation, the $f(T)$ field equations are not invariant under local Lorentz transformations, and thus the theory does not inherit the causal structure of special relativity. A locally Lorentz covariant $f(T)$…
G\"odel universe, one of the most interesting exact solutions predicted by General Relativity, describes a homogeneous rotating universe containing naked closed time-like curves (CTCs). It was shown that such CTCs are the consequence of the…
We propose the most general modified first-order Ho\v{r}ava-Lifshitz (HL) gravity, whose action does not contain time derivatives higher than the second order. The Hamiltonian structure of this theory is studied in all the details in the…
Violations of Lorentz (and specifically boost) invariance can make gravity renormalizable in the ultraviolet, as initially noted by Ho\v{r}ava, but are increasingly constrained in the infrared. At low energies, Ho\v{r}ava gravity is…
Ho\v{r}ava gravity is a Lorentz-violating modification of general relativity (GR) with a preferred spacelike foliation. Observational evidence has put strong constraints on the parameter values in this model, so that the remaining viable…
Both projectable and non-projectable versions of Horava-Lifshitz gravity face serious challenges. In the non-projectable version, the constraint algebra is seemingly inconsistent. The projectable version lacks a local Hamiltonian…
For any fundamental quantum field theory, unitarity, renormalizability, and relativistic invariance are considered to be essential properties. Unitarity is inevitably connected to the probabilistic interpretation of the quantum theory,…
We investigate the interplay between Horava-Lifshitz (HL) gravity and more general theories where the local Hamiltonian constraint is lost, for example due to the time variability of the Lagrangian (e.g. via its parameters) where time is…
This article reviews basic construction and cosmological implications of a power-counting renormalizable theory of gravitation recently proposed by Horava. We explain that (i) at low energy this theory does not exactly recover general…
A proposal for a power-counting renormalizable theory of quantum gravity at a Lifshitz point was recently put forth by Horava (arXiv:0901.3775), and has been since dubbed as Horava-Lifshitz gravity. The theory explicitly breaks Lorentz…
In this note, we discuss the renormalizability of Horava-Lifshitz-type gravity theories. Using the fact that Horava-Lifshitz gravity is very closely related to the stochastic quantization of topologically massive gravity, we show that the…
We study causal properties of the recently found rotating black-hole solution in the low-energy sector of Horava gravity as a viable Lorentz-violating (LV) gravity in four dimensions with the LV Maxwell field and a cosmological constant…
Recently Ho$\breve{r}$ava proposed a non-relativistic renormalisable theory of gravitation. When restricted to satisfy the condition of detailed balance, this theory is intimately related to topologically massive gravity in three…
Recently, Ho$\breve{r}$ava proposed a non-relativistic renormalizable theory of gravity which is essentially a field theoretic model for a UV complete theory of gravity and reduces to Einstein gravity with a non-vanishing cosmological…
The standard $\Lambda$CDM model despite its agreement with observational data still has some issues unaddressed, lie the problem of initial singularity. Solving that problem usually requires modifications of general relativity. However,…