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We study the behaviour of Bianchi class A universes containing an ultra-stiffisotropic ghost field and a fluid with anisotropic pressures which is alsoultra-stiff on the average. This allows us to investigate whether cyclicuniverse scenarios, like the ekpyrotic model, do indeed lead to isotropisationon approach to a singularity (or bounce) in the presence of dominantultra-stiff pressure anisotropies. We specialise to consider the closed Bianchitype IX universe and show that when the anisotropic pressures are stiffer onaverage than any isotropic ultra-stiff fluid then, if they dominate on approachto the singularity, it will be anisotropic. We include an isotropic ultra-stiffghost fluid with negative energy density in order to create a cosmologicalbounce at finite volume in the absence of the anisotropic fluid. When thedominant anisotropic fluid is present it leads to an anisotropic cosmologicalsingularity rather than an isotropic bounce. The inclusion of anisotropicstresses generated by collisionless particles in an anisotropically expandinguniverse is therefore essential for a full analysis of the consequences of acosmological bounce or singularity in cyclic universes.

Evolution of initially contracting Bianchi Class A models in the presence of an ultra-stiff anisotropic pressure fluid