Isotropization of Slowly Expanding Spacetimes

Abstract

We show that the homogeneous, massless Einstein-Vlasov system with toroidal spatial topology and diagonal Bianchi type I symmetry for initial data close to isotropic data isotropizes towards the future and in particular asymptotes to a radiative Einstein-deSitter model. We use an energy method to obtain quantitative estimates on the rate of isotropization in this class of models.

arXiv commentAdded references, argument in section 3 revised

References in corpus (19)

• The Einstein-Vlasov System/Kinetic Theory
• Cosmological models and centre manifold theory
• Dynamics of spatially homogeneous solutions of the Einstein-Vlasov equations which are locally rotationally symmetric
• Dynamics of spatially homogeneous locally rotationally symmetric solutions of the Einstein-Vlasov equations
• Flat Spots: topological signatures of an open universe in COBE sky maps
• Bianchi Cosmologies with Anisotropic Matter: Locally Rotationally Symmetric Models
• The Isotropy of Compact Universes
• The initial singularity in solutions of the Einstein-Vlasov system of Bianchi type I
• Dynamics of the spatially homogeneous Bianchi type I Einstein-Vlasov equations
• All Universes Great and Small
• Isotropization of non-diagonal Bianchi I spacetimes with collisionless matter at late times assuming small data
• Future global existence and asymptotic behaviour of solutions to the Einstein-Boltzmann system with Bianchi I symmetry
• Dynamics of Bianchi type I solutions of the Einstein equations with anisotropic matter
• Future non-linear stability for solutions of the Einstein-Vlasov system of Bianchi types II and VI${}_0$
• Cosmology: the search for twenty-four (or more) functions
• Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI${}_0$
• Kantowski-Sachs cosmology with Vlasov matter
• Dynamics of locally rotationally symmetric Bianchi type VIII cosmologies with anisotropic matter
• Isotropization of solutions of the Einstein-Vlasov system with Bianchi V symmetry

Cited by in corpus (10)

• Finite Action Principle Revisited
• On the oscillations and future asymptotics of locally rotationally symmetric Bianchi type III cosmologies with a massive scalar field
• Averaging Generalized Scalar Field Cosmologies I: Locally Rotationally Symmetric Bianchi III and open Friedmann-Lemaître-Robertson-Walker models
• Averaging Generalized Scalar Field Cosmologies II: Locally Rotationally Symmetric Bianchi I and flat Friedmann-Lemaître-Robertson-Walker models
• Stable cosmologies with collisionless charged matter
• Future attractors of Bianchi types II and V cosmologies with massless Vlasov matter
• On the future of solutions to the massless Einstein-Vlasov system in a Bianchi I cosmology
• On almost Ehlers-Geren-Sachs theorems
• Relativistic BGK model for massless particles in the FLRW spacetime
• Future of Bianchi I magnetic cosmologies with kinetic matter