Horava-Lifshitz Cosmology: A Review

TL;DR

This review discusses Horava-Lifshitz gravity's construction, its cosmological implications such as bouncing universes and scale-invariant perturbations, and addresses issues like scalar graviton stability and the lambda->1 limit.

Contribution

It provides a comprehensive overview of Horava-Lifshitz cosmology, highlighting its unique features and stability conditions, and clarifies the behavior of scalar graviton and the lambda parameter.

Findings

Higher spatial curvature enables bouncing and cyclic universes.

Scale-invariant perturbations arise without inflation.

Non-perturbative continuity of lambda->1 limit proven.

Abstract

This article reviews basic construction and cosmological implications of a power-counting renormalizable theory of gravitation recently proposed by Horava. We explain that (i) at low energy this theory does not exactly recover general relativity but instead mimic general relativity plus dark matter; that (ii) higher spatial curvature terms allow bouncing and cyclic universes as regular solutions; and that (iii) the anisotropic scaling with the dynamical critical exponent z=3 solves the horizon problem and leads to scale-invariant cosmological perturbations even without inflation. We also comment on issues related to an extra scalar degree of freedom called scalar graviton. In particular, for spherically-symmetric, static, vacuum configurations we prove non-perturbative continuity of the lambda->1+0 limit, where lambda is a parameter in the kinetic action and general relativity has the value lambda=1. We also derive the condition under which linear instability of the scalar graviton does not show up.