Advances in Theoretical and Mathematical Physics

Volume 26 (2022)

Number 7

Bifurcations and chaos in Hořava–Lifshitz cosmology

Pages: 2095 – 2211



Juliette Hell (Institut für Mathematik, Freie Universität Berlin, Germany)

Phillipo Lappicy (ICMC, Universidade de São Paulo, São Carlos, Brazil; and Instituto Superior Técnico, Universidade de Lisboa, Portugal)

Claes Uggla (Department of Physics, Karlstad University, Karlstad, Sweden)


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.

Published 30 August 2023