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 VI 0 , VII 0 (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.