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Kasner and Mixmaster behavior in universes with equation of state w \ge 1

Joel K. Erickson·Daniel H. Wesley·Paul J. Steinhardt·Neil Turok
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Abstract

We consider cosmological models with a scalar field with equation of state $w\ge 1$ 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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Joel K. Erickson, Daniel H. Wesley, Paul J. Steinhardt, Neil Turok. 2004-03-27. Kasner and Mixmaster behavior in universes with equation of state w \ge 1. https://doi.org/10.1103/physrevd.69.063514

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