Chaos in spatially homogeneous Ho\v{r}ava-Lifshitz subcritical cosmologies

TL;DR

This paper investigates chaos in spatially homogeneous Hořava-Lifshitz cosmologies, demonstrating that the Kasner map exhibits chaos in a broad class of models when the parameter v is between 0 and 1/2, indicating complex dynamics near GR.

Contribution

It proves the chaos of the Kasner map in subcritical Hořava-Lifshitz gravity models, extending understanding of chaotic behavior in modified gravity theories.

Findings

Kasner map is chaotic for v in (0,1/2)

Chaos persists despite multivalued Kasner map in subcritical regime

Chaos occurs in a broad class of HL gravity models

Abstract

We consider spatially homogeneous models in Ho\v{r}ava-Lifshitz (HL) gravity that perturbs General Relativity (GR) by a parameter $v\in (0,1)$ such that GR occurs at $v=1/2$. We prove that the induced Kasner map is chaotic for a broad class of modified HL gravity models, when $v\in (0,1/2)$, despite the fact that the Kasner map is multivalued in such subcritical regime.