Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant

Abstract

The behaviour of expanding cosmological models with collisionless matter and a positive cosmological constant is analysed. It is shown that under the assumption of plane or hyperbolic symmetry the area radius goes to infinity, the spacetimes are future geodesically complete, and the expansion becomes isotropic and exponential at late times. This proves a form of the cosmic no hair theorem in this class of spacetimes.

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• Cosmological solutions of the Vlasov-Einstein system with spherical, plane, and hyperbolic symmetry
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Cited by in corpus (17)

• Dynamics of $k$-essence
• Intermediate inflation and the slow-roll approximation
• Accelerated cosmological expansion due to a scalar field whose potential has a positive lower bound
• The Einstein-Vlasov System/Kinetic Theory
• The Einstein-Vlasov system/Kinetic theory
• Theorems on existence and global dynamics for the Einstein equations
• Power-law Inflation in Spacetimes without Symmetry
• Asymptotic isotropization in inhomogeneous cosmology
• Strong cosmic censorship for surface-symmetric cosmological spacetimes with collisionless matter
• Global Existence of Solutions for the Einstein-Boltzmann System in a Bianchi Type I Space-Time
• Isotropic cosmological singularities in spatially-homogeneous models with a cosmological constant
• 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
• The problem of a self-gravitating scalar field with positive cosmological constant
• Cosmic no-hair in spherically symmetric black hole spacetimes
• Structure of solutions near the initial singularity for the surface-symmetric Einstein-Vlasov system
• Future global non-linear stability of surface symmetric solutions of the Einstein-Vlasov system with a cosmological constant