Theoretical status of Horava gravity

I’ll review the models of quantum gravity postulating invariance with respect to anisotropic (Lifshitz) scaling in the deep ultraviolet domain. At low energies they reduce to scalar-tensor gravity, with a timelike gradient of the scalar field breaking local Lorentz invariance. The models come in two versions differing by the dynamics in the scalar sector. The first, projectable, model has been shown to be perturbatively renormalizable and the full renormalization group (RG) flow of its marginal operators has been computed. The flow possesses a number of asymptotically free fixed points with one of them being connected by RG trajectories to the region of the parameter space where the kinetic term of the theory acquires the general relativistic form. The gravitational coupling exhibits non-monotonic behavior along the flow, vanishing both in the ultraviolet and the infrared. I’ll mention the challenges facing the model in the infrared domain. The second, non-projectable, model is known to reproduce the phenomenology of general relativity in a certain region of parameters. Full proof of its renormalizability is still missing due to its complicated structure. I’ll review recent progress towards constructing such proof.