Quantum gravity without Lorentz invariance

TL;DR

This paper explores a variant of Horava's quantum gravity model that abandons detailed balance and restores parity invariance, analyzing its classical equations, graviton propagators, and cosmological implications.

Contribution

It introduces a generalized Horava gravity model without detailed balance, restoring parity, and examines its classical and cosmological properties.

Findings

Explicit classical equations of motion derived

Graviton propagators analyzed around Minkowski space

Higher-derivative terms can mimic radiation and stiff matter

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.