Ho\v{r}ava-Lifshitz gravity inspired Bianchi-II cosmology and the mixmaster universe

TL;DR

This paper explores Bianchi-II cosmology inspired by Hořava-Lifshitz gravity, providing exact solutions, analyzing singularities, and relating findings to the mixmaster universe, suggesting oscillatory approach to singularity.

Contribution

It offers new exact solutions for Hořava-Lifshitz Bianchi-II models and connects these to mixmaster universe dynamics, highlighting potential oscillatory singularity behavior.

Findings

Exact solutions for toy models with cubic and quadratic spatial curvature terms.

Identification of exotic singularities in the toy models.

Evidence supporting oscillatory approach to singularity in Hořava-Lifshitz gravity.

Abstract

We study different aspects of the Ho\v{r}ava-Lifshitz inspired Bianchi-II cosmology and its relations with the mixmaster universe model. First, we present exact solutions for a toy model, where only the cubic in spatial curvature terms are present in the action; then we briefly discuss some exotic singularities, which can appear in this toy model. We study also the toy model where only the quadratic in spatial curvature terms are present in the action. We establish relations between our results and those obtained by using the Hamiltonian formalism. Finally, we apply the results obtained by studying Bianchi-II cosmology to describe the evolution of the mixmaster universe in terms of the Belinsky-Khalatnikov-Lifshitz formalism. Generally, our analysis gives some arguments in favour of the existence of the oscillatory approach to the singularity in a universe governed by the Ho\v{r}ava-Lifshitz type gravity.