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Homoclinic chaos and energy condition violation

J. Mark Heinzle·N. Rohr·C. Uggla
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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 $ρ>0$ that evolve through the singularity and beyond as solutions with negative matter energy density $ρ<0$. 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.

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J. Mark Heinzle, N. Rohr, C. Uggla. 2006-07-31. Homoclinic chaos and energy condition violation. https://doi.org/10.1103/physrevd.74.061502

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