The Cosmic No-Hair Theorem and the Nonlinear Stability of Homogeneous Newtonian Cosmological Models

Abstract

The validity of the cosmic no-hair theorem is investigated in the context of Newtonian cosmology with a perfect fluid matter model and a positive cosmological constant. It is shown that if the initial data for an expanding cosmological model of this type is subjected to a small perturbation then the corresponding solution exists globally in the future and the perturbation decays in a way which can be described precisely. It is emphasized that no linearization of the equations or special symmetry assumptions are needed. The result can also be interpreted as a proof of the nonlinear stability of the homogeneous models. In order to prove the theorem we write the general solution as the sum of a homogeneous background and a perturbation. As a by-product of the analysis it is found that there is an invariant sense in which an inhomogeneous model can be regarded as a perturbation of a unique homogeneous model. A method is given for associating uniquely to each Newtonian cosmological model with compact spatial sections a spatially homogeneous model which incorporates its large-scale dynamics. This procedure appears very natural in the Newton-Cartan theory which we take as the starting point for Newtonian cosmology.

arXiv comment16 pages, MPA-AR-94-2

References in corpus (1)

• Global existence of classical solutions to the Vlasov-Poisson system in a three dimensional, cosmological setting

Cited by in corpus (36)

• Homogeneous cosmologies with cosmological constant
• The Einstein-Vlasov System/Kinetic Theory
• Newtonian Cosmology in Lagrangian Formulation: Foundations and Perturbation Theory
• Theorems on existence and global dynamics for the Einstein equations
• Global existence and asymptotic behaviour in the future for the Einstein-Vlasov system with positive cosmological constant
• The Stability of the Irrotational Euler-Einstein System with a Positive Cosmological Constant
• Exactly Soluble Sector of Quantum Gravity
• Stabilizing relativistic fluids on spacetimes with non-accelerated expansion
• Cosmic Equilibration: A Holographic No-Hair Theorem from the Generalized Second Law
• Cosmological Newtonian limits on large spacetime scales
• A sharp local blow-up condition for Euler-Poisson equations with attractive forcing
• Nonlinear stability of homogeneous models in Newtonian cosmology
• On the Newtonian Limit of the Weyl Tensor
• Future global stability for relativistic perfect fluids with linear equations of state $p=K\rho$ where $1/3<K<1/2$
• Newtonian Limits of Isolated Cosmological Systems on Long Time Scales
• Future stability of the FLRW spacetime for a large class of perfect fluids
• Exponential Decay for Small Non-Linear Perturbations of Expanding Flat Homogeneous Cosmologies
• Cosmological post-Newtonian expansions to arbitrary order
• Local and global existence theorems for the Einstein equations
• The non-isentropic Einstein-Euler system written in a symmetric hyperbolic form
• Towards a no hair theorem for higher order gravity
• The Stability of Relativistic Fluids in Linearly Expanding Cosmologies
• On the stability of relativistic perfect fluids with linear equations of state $p=K\rho$ where $1/3<K<1$
• Future dynamics of FLRW for the massless-scalar field system with positive cosmological constant
• Critical thresholds in 1D pressureless Euler-Poisson systems with varying background
• Slowly expanding stable dust spacetimes
• Rigorous proof of slightly nonlinear Jeans instability in the expanding Newtonian universe
• Blowup for $C^2$ Solutions of the N-dimensional Euler-Poisson Equations in Newtonian Cosmology
• Critical Thresholds in 2D Restricted Euler-Poisson Equations
• Critical Thresholds in Euler-Poisson Equations
• Critical thresholds in the Euler-Poisson-alignment system
• The linear stability of the Einstein-Euler system on negative Einstein spaces
• The Global Future Stability of the FLRW Solutions to the Dust-Einstein System with a Positive Cosmological Constant
• On Twisted Spacetimes: a new class of Galilean cosmological models
• Necessary conditions for blow-up solutions to the restricted Euler--Poisson equations
• On the Riccati dynamics of the Euler-Poisson equations with zero background state