Horava-Lifshitz Cosmology: A Review

TL;DR

Hořava-Lifshitz gravity offers a power-counting renormalizable route to quantum gravity by sacrificing full Lorentz invariance and employing Lifshitz scaling with $z=3$ in the UV. The paper surveys the theory’s construction, its global Hamiltonian constraint leading to dark matter as an integration constant, and cosmological consequences including bouncing/cyclic histories and a mechanism for scale-invariant perturbations without inflation, along with the scalar graviton issues and nonperturbative continuity of the $\lambda \to 1^+$ limit. It highlights the need for RG analyses, potential mechanisms to restore low-energy Lorentz invariance, and extensions with larger symmetry, as well as the broader implications for early-universe cosmology and observable signatures. Overall, the work outlines a coherent framework where UV-renormalizable gravity yields distinctive cosmological scenarios and poses clear theoretical and phenomenological questions for future study, such as the fate of the RG flow of $\lambda$ and the viability of the projectable theory in realistic settings.

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.

Figures (4)

• Figure 1: $V(a)$ for $\Lambda=0.4$ and $8\pi GC=10$. If the universe is initially contracting then it bounces and expands.
• Figure 2: $V(a)$ for $\Lambda=0$ and $8\pi GC=10$. This allows a series of expansion and contraction, i.e. a cyclic universe.
• Figure 3: $V(a)$ for $\Lambda=15/64$ and $8\pi GC=17/4$. This allows a static universe at $a=2$ but it is unstable. A bouncing universe is also allowed.
• Figure 4: $V(a)$ for $\Lambda=0$ and $C=4$. This allows a stable static universe at $a=1$.