Mixmaster universe in Horava-Lifshitz gravity

TL;DR

This paper explores the behavior of anisotropic cosmologies in Horava-Lifshitz gravity, revealing differences from general relativity, especially in the dominance of the Cotton tensor potential and the nature of early universe dynamics.

Contribution

It provides a Hamiltonian analysis of Bianchi type IX cosmologies in Horava-Lifshitz gravity, highlighting the role of the Cotton tensor and the altered chaotic behavior near singularities.

Findings

Dominance of Cotton tensor potential at small volumes

Early universe described by fixed-energy particle motion

Chaotic behavior differs from general relativity, with non-ergodic evolution at certain energies

Abstract

We consider spatially homogeneous (but generally non-isotropic) cosmologies in the recently proposed Horava-Lifshitz gravity and compare them to those of general relativity using Hamiltonian methods. In all cases, the problem is described by an effective point particle moving in a potential well with exponentially steep walls. Focusing on the closed-space cosmological model (Bianchi type IX), the mixmaster dynamics is now completely dominated by the quadratic Cotton tensor potential term for very small volume of the universe. Unlike general relativity, where the evolution towards the initial singularity always exhibits chaotic behavior with alternating Kasner epochs, the anisotropic universe in Horava-Lifshitz gravity (with parameter lambda > 1/3) is described by a particle moving in a frozen potential well with fixed (but arbitrary) energy E. Alternating Kasner epochs still provide a good description of the early universe for very large E, but the evolution appears to be non-ergodic. For very small E there are harmonic oscillations around the fully isotropic model. The question of chaos remains open for intermediate energy levels.