Vector Field Induced Chaos in Multi-dimensional Homogeneous Cosmologies

TL;DR

This paper demonstrates that vector fields fundamentally influence the singularity structure in multidimensional homogeneous cosmologies, leading to universal oscillatory behavior and new dynamics in Kasner regimes.

Contribution

It introduces a comprehensive analysis of how vector fields induce chaos and oscillations in higher-dimensional cosmological models, extending known 4D results.

Findings

Oscillatory regimes exist in all dimensions with vector fields.

Derived Poincaré return map for Kasner indexes.

Identified rotation rules for Kasner vectors.

Abstract

We show that in multidimensional gravity vector fields completely determine the structure and properties of singularity. It turns out that in the presence of a vector field the oscillatory regime exists for any number of spatial dimensions and for all homogeneous models. We derive the Poincar\'e return map associated to the Kasner indexes and fix the rules according to which the Kasner vectors rotate. In correspondence to a 4-dimensional space time, the oscillatory regime here constructed overlap the usual Belinski-Khalatnikov-Liftshitz one.