Abstract
We consider cosmological models with a scalar field with equation of state $w>~1$ that contract towards a big crunch singularity, as in recent cyclic and ekpyrotic scenarios. We show that chaotic mixmaster oscillations due to anisotropy and curvature are suppressed, and the contraction is described by a homogeneous and isotropic Friedmann equation if $w>1.$ We generalize the results to theories where the scalar field couples to p forms and show that there exists a finite value of w, depending on the p-forms, such that chaotic oscillations are suppressed. We show that ${Z}_{2}$ orbifold compactification also contributes to suppressing chaotic behavior. In particular, chaos is avoided in contracting heterotic M-theory models if $w>1$ at the crunch.
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