Theoretical status of quantum gravity with anisotropic scaling

I’ll review the approach to quantum gravity postulating invariance with respect to anisotropic (Lifshitz) scaling in the deep ultraviolet domain. At low energies it leads to scalar-tensor gravity, with a timelike gradient of the scalar field breaking local Lorentz invariance. There are two types of models differing by the dynamics in the scalar sector. The first, projectable, model has been shown to be perturbatively renormalizable and the full …