Oscillatory regime in the Multidimensional Homogeneous Cosmological Models Induced by a Vector Field

TL;DR

This paper demonstrates that vector fields in multidimensional homogeneous cosmological models induce an oscillatory regime near singularities across all spatial dimensions, extending known 4D behaviors.

Contribution

It introduces a comprehensive analysis of how vector fields influence singularity structure, establishing the existence of oscillatory regimes in all dimensions and deriving the associated Kasner dynamics.

Findings

Oscillatory regimes exist in all spatial dimensions with vector fields.

Derived the Poincaré return map for Kasner indexes.

Identified rotation rules for Kasner vectors in these models.

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 in all spatial dimensions and for all homogeneous models. By analyzing the Hamiltonian equations 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.