Bifurcations and Chaos in Hořava-Lifshitz Cosmology

Abstract

The nature of generic spacelike singularities in general relativity is connected with first principles, notably Lorentzian causal structure, scale invariance and general covariance. To bring a new perspective on how these principles affect generic spacelike singularities, we consider the initial singularity in spatially homogeneous Bianchi type VIII and IX vacuum models in Hořava-Lifshitz gravity, where relativistic first principles are replaced with anisotropic scalings of Lifshitz type. Within this class of models, General Relativity is shown to be a bifurcation where chaos becomes generic. To describe the chaotic features of generic singularities in Hořava-Lifshitz cosmology, we introduce symbolic dynamics within Cantor sets and iterated function systems.

93 Pages, 21 Figures

Cited by in corpus (2)

• Cosmological dynamics and bifurcation analysis of the general non-minimally coupled scalar field models
• Periodic orbits in Hořava-Lifshitz cosmologies