Matter and dynamics in closed cosmologies

Abstract

To systematically analyze the dynamical implications of the matter content in cosmology, we generalize earlier dynamical systems approaches so that perfect fluids with a general barotropic equation of state can be treated. We focus on locally rotationally symmetric Bianchi type IX and Kantowski-Sachs orthogonal perfect fluid models, since such models exhibit a particularly rich dynamical structure and also illustrate typical features of more general cases. For these models, we recast Einstein's field equations into a regular system on a compact state space, which is the basis for our analysis. We prove that models expand from a singularity and recollapse to a singularity when the perfect fluid satisfies the strong energy condition. When the matter source admits Einstein's static model, we present a comprehensive dynamical description, which includes asymptotic behavior, of models in the neighborhood of the Einstein model; these results make earlier claims about ``homoclinic phenomena and chaos'' highly questionable. We also discuss aspects of the global asymptotic dynamics, in particular, we give criteria for the collapse to a singularity, and we describe when models expand forever to a state of infinite dilution; possible initial and final states are analyzed. Numerical investigations complement the analytical results.

23 pages, 24 figures (compressed), LaTeX

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• A new proof of the Bianchi type IX attractor theorem
• The Instabilities of Bianchi Type IX Einstein Static Universes
• The recollapse problem of closed FRW models in higher-order gravity theories
• Dynamics of Einstein-Aether Scalar field Cosmology
• Cosmological models from a dynamical systems perspective
• Hamiltonian Dynamics of Spatially-Homogeneous Vlasov-Einstein Systems
• Dynamics and chaos in the unified scalar field Cosmology
• Scalar field deformations of Lambda-CDM cosmology
• Monotonic functions in Bianchi models: Why they exist and how to find them
• $f(T,B)$ gravity in a Friedmann-Lema\^ıtre-Robertson-Walker universe with nonzero spatial curvature
• On closed cosmological models that satisfy the strong energy condition but do not recollapse
• Dynamics of locally rotationally symmetric Bianchi type VIII cosmologies with anisotropic matter
• On The Dynamics of a Closed Viscous Universe
• Bianchi type I models with two tilted fluids
• Homoclinic chaos and energy condition violation
• Perfect fluids and generic spacelike singularities
• Dynamics and chaos in the unified scalar field cosmology II. System in a finite box
• Homoclinic Chaos in Axisymmetric Bianchi-IX cosmological models with an "ad hoc" quantum potential