Periodic orbits in Hořava–Lifshitz cosmologies

We consider spatially homogeneous Hořava–Lifshitz models that perturb General Relativity (GR) by a parameter v∈(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 I (Kasner circle of equilibria), type II (heteroclinics that induce the Kasner map) and type VI0,VII0 (further heteroclinics). For type VIII and IX, we use a computer-assisted approach to prove the existence of periodic orbits which are far from the Mixmaster attractor. Therefore we obtain a new behaviour which is not described by the BKL picture of bouncing Kasner-like states

Periodic orbits in Ho\v{r}ava-Lifshitz cosmologies

We consider spatially homogeneous Ho\v{r}ava-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 I (Kasner circle of equilibria), type II (heteroclinics that induce the Kasner map) and type $\mathrm{VI_0},\mathrm{VII_0}$ (further heteroclinics). For type VIII and IX, we prove the existence of periodic orbits which are far from the Mixmaster attractor, and thereby yield a new behaviour which is not described by the BKL picture.Comment: 19 pages, 7 figure