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

TL;DR

This paper demonstrates that in cosmological models with scalar fields having an equation of state w ≥ 1, chaotic mixmaster oscillations are suppressed during contraction, leading to more homogeneous and isotropic behavior near singularities.

Contribution

It generalizes the suppression of chaos in contracting universes to models with scalar fields coupled to p-forms and orbifold compactifications, identifying conditions for chaos avoidance.

Findings

Chaotic oscillations are suppressed for w > 1.

Suppression of chaos extends to scalar fields coupled to p-forms.

Orbifold compactification further reduces chaotic behavior.

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.