Homoclinic chaos and energy condition violation

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.

arXiv comment4 pages, RevTeX

References in corpus (8)

• The Bianchi IX attractor
• The past attractor in inhomogeneous cosmology
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• Homoclinic chaos in the dynamics of a general Bianchi IX model
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Cited by in corpus (4)

• Free motion around black holes with discs or rings: between integrability and chaos - II
• Free motion around black holes with discs or rings: between integrability and chaos - I
• Hamiltonian Dynamics of Spatially-Homogeneous Vlasov-Einstein Systems
• Chaotic dynamics of the Bianchi IX universe in Gauss-Bonnet gravity