Oscillating Bianchi IX Universe in Horava-Lifshitz Gravity

TL;DR

This paper investigates the classical dynamics of a vacuum Bianchi IX universe within Hořava-Lifshitz gravity, revealing diverse cosmological behaviors including oscillations, bounces, big crunches, and de Sitter expansion, depending on initial anisotropy and cosmological constant.

Contribution

It provides a detailed analysis of anisotropic universe evolution in HL gravity, highlighting the dependence on initial conditions and the presence of chaotic behavior.

Findings

Oscillating and bounce universes for small anisotropy.

Universe ends with big crunch for large anisotropy and non-positive b3.

De Sitter expansion occurs for positive b3 with certain initial conditions.

Abstract

We study a vacuum Bianchi IX universe in the context of Ho\v{r}ava-Lifshitz (HL) gravity. In particular, we focus on the classical dynamics of the universe and analyze how anisotropy changes the history of the universe. For small anisotropy, we find an oscillating universe as well as a bounce universe just as the case of the Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. However, if the initial anisotropy is large, we find the universe which ends up with a big crunch after oscillations if a cosmological constant $\Lambda$ is zero or negative. For $\Lambda>0$, we find a variety of histories of the universe, that is de Sitter expanding universe after oscillations in addition to the oscillating solution and the previous big crunch solution. This fate of the universe shows sensitive dependence of initial conditions, which is one of the typical properties of a chaotic system. If the initial anisotropy is near the upper bound, we find the universe starting from a big bang and ending up with a big crunch for $\Lambda\leq 0$, while de Sitter expanding universe starting from a big bang for $\Lambda>0$.