There has been a significant surge of interest in Hořava's model for 3+1 dimensional quantum gravity, this model being based on anisotropic scaling at a z = 3 Lifshitz point. Hořava'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 [hep-th]], we discuss in more detail our variant of Hořava's model. In contrast to Hořava's original model, we abandon ``detailed balance'' and restore parity invariance. We retain, however, Hořava'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.
Journal of High Energy Physics
- Pub Date:
- October 2009
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology
- 36 pages. V2: three references added, technical changes to gauge-fixing discussion, minor edits. V3: some additional discussion and references, closely matches final published version