Homoclinic chaos and energy condition violation

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 nontilted 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 rotationally symmetric we demonstrate that the construction of extensions through the singularity, which is required for homoclinic chaos, is not possible in general.