Periodic orbits in Hořava-Lifshitz cosmologies

Abstract

We consider spatially homogeneous Hořava-Lifshitz (HL) models that perturb General Relativity (GR) by a parameter $v\in (0,1)$ such that GR occurs at $v=1/2$. We describe the dynamics for the extremal case $v=0$, which possess the usual Bianchi hierarchy: type $\mathrm{I}$ (Kasner circle of equilibria), type $\mathrm{II}$ (heteroclinics that induce the Kasner map) and type $\mathrm{V}{\mathrm{I}}_0,\mathrm{VI}{\mathrm{I}}_0$ (further heteroclinics). For type $\mathrm{VIII}$ and $\mathrm{IX}$, we use a computer-assisted approach to prove the existence of periodic orbits which are far from the Mixmaster attractor and thereby we obtain a new behaviour which is not described by the BKL picture of bouncing Kasner-like states.

21 pages, 7 figures. arXiv admin note: text overlap with arXiv:2012.07614

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