Quantum gravity without Lorentz invariance

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, Phys. Rev. Lett. 102 (2009) 251601 [arXiv: 0904.4464 [hepth]], 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.