Quantum gravity without Lorentz invariance

TL;DR

This paper develops a Lorentz-violating, Horava-like quantum gravity model that foregoes detailed balance but retains a global projectability condition. It constructs the full classical action in ADM form, derives the Hamiltonian, super-momentum, and dynamical equations, and analyzes linearized spin-0 and spin-2 graviton propagators around Minkowski space, revealing a sixth-order dispersion for both modes with different coupling dependencies. The authors then apply the framework to FLRW cosmology, showing higher-spatial-curvature terms can mimic dark radiation and stiff matter, and derive modified Friedmann equations with a single parameterized departure from GR. While offering a potentially viable path to UV-complete gravity with tunable Lorentz violation scales, the work highlights significant concerns about the propagating spin-0 mode and discusses prospects for relaxing projectability and confronting the model with experimental bounds.

Abstract

There has been a significant surge of interest in Horava's model for 3+1 dimensional quantum gravity, this model being based on anisotropic scaling at a z=3 Lifshitz point. Horava's model, and its variants, show dramatically improved ultra-violet behaviour at the cost of exhibiting violation of Lorentz invariance at ultra-high momenta. Following up on our earlier note, [arXiv:0904.4464 [hep-th]], we discuss in more detail our variant of Horava's model. In contrast to Horava's original model, we abandon "detailed balance" and restore parity invariance. We retain, however, Horava's "projectability condition" and explore its implications. Under these conditions, we explicitly exhibit the most general model, and extract the full classical equations of motion in ADM form. We analyze both spin-2 and spin-0 graviton propagators around flat Minkowski space. We furthermore analyze the classical evolution of FLRW cosmologies in this model, demonstrating that the higher-derivative spatial curvature terms can be used to mimic radiation fluid and stiff matter. We conclude with some observations concerning future prospects.