Homoclinic chaos and energy condition violation

TL;DR

This paper links homoclinic chaos in certain cosmological models to unphysical assumptions about negative energy densities, showing that such chaos is an artifact of these assumptions and does not occur under physically realistic conditions.

Contribution

It demonstrates that homoclinic chaos in Bianchi type IX models arises from unphysical negative energy solutions, and shows that such chaos is absent when positive matter energy density is maintained.

Findings

Homoclinic chaos requires negative energy densities, which are unphysical.

Homoclinic chaos is absent when dust particles retain positive mass.

Extensions through the singularity are generally not possible in non-symmetric models.

Abstract

In this letter we discuss the connection between so-called homoclinic chaos and the violation of energy conditions in locally rotationally symmetric Bianchi type IX models, where the matter is assumed to be non-tilted dust and a positive cosmological constant. We show that homoclinic chaos in these models is an artifact of unphysical assumptions: it requires that there exist solutions with positive matter energy density $\rho>0$ that evolve through the singularity and beyond as solutions with negative matter energy density $\rho<0$. Homoclinic chaos is absent when it is assumed that the dust particles always retain their positive mass.In addition, we discuss more general models: for solutions that are not locally rotionally symmetric we demonstrate that the construction of extensions through the singularity, which is required for homoclinic chaos, is not possible in general.