Cosmic No Hair for Collapsing Universes

TL;DR

The paper demonstrates that contracting homogeneous universes with ultra-stiff fluids tend to become flat and isotropic near the big crunch, and explores implications for collapsing Bianchi type IX universes in M*-theory.

Contribution

It proves the universal approach to flat, isotropic states in collapsing Bianchi cosmologies with ultra-stiff fluids and analyzes supersymmetric attractors in M*-theory models.

Findings

Contracting Bianchi universes asymptote to flat, isotropic states.

Supersymmetric attractor solutions exist in collapsing Bianchi IX models.

The results connect cosmological collapse with string/M-theory frameworks.

Abstract

It is shown that all contracting, spatially homogeneous, orthogonal Bianchi cosmologies that are sourced by an ultra-stiff fluid with an arbitrary and, in general, varying equation of state asymptote to the spatially flat and isotropic universe in the neighbourhood of the big crunch singularity. This result is employed to investigate the asymptotic dynamics of a collapsing Bianchi type IX universe sourced by a scalar field rolling down a steep, negative exponential potential. A toroidally compactified version of M*-theory that leads to such a potential is discussed and it is shown that the isotropic attractor solution for a collapsing Bianchi type IX universe is supersymmetric when interpreted in an eleven-dimensional context.