Horava-Lifshitz Cosmology

TL;DR

The work investigates cosmology within Horava-Lifshitz gravity, a UV-renormalizable theory with anisotropic scaling $t\to \ell^z t$, $x^i\to \ell x^i$ and reduced diffeomorphism invariance, which flows to GR in the IR at $\lambda\to1$. The authors derive the non-relativistic matter actions (scalars and vectors) and the full gravitational dynamics, showing that higher-spatial-derivative terms introduce novel contributions to the Friedmann equation and can trigger a non-singular bounce. In the UV-dominated regime, they argue that six-derivative terms render perturbations scale-invariant and allow horizon growth without inflation, via a dispersion relation $E^2\approx \ell^4 k^6/a^6$, while the IR limit recovers standard GR with $G$ and $\Lambda_E$. The paper outlines a qualitative perturbation framework and highlights the potential of HL cosmology to address horizon/flatness problems and singularities, while acknowledging open issues in the transition to the IR and in the detailed perturbation evolution.

Abstract

The cosmological equations suggested by the non-relativistic renormalizable gravitational theory proposed by Hořava are considered. It is pointed out that the early universe cosmology has features that may give an alternative to inflation and the theory may be able to escape singularities.