Newtonian Limits of Isolated Cosmological Systems on Long Time Scales

Abstract

We establish the existence of $1$-parameter families of $\epsilon$-dependent solutions to the Einstein-Euler equations with a positive cosmological constant $\Lambda >0$ and a linear equation of state $p={\epsilon }^{2}K\rho$, $0<K\le 1/3$, for the parameter values $0<\epsilon <{\epsilon }_0$. These solutions exist globally to the future, converge as $\epsilon \searrow 0$ to solutions of the cosmological Poison-Euler equations of Newtonian gravity, and are inhomogeneous non-linear perturbations of FLRW fluid solutions.

58 pages. Agrees with published version. Note the title has been changed. Old title "Cosmological Newtonian limits on long time scales"; New title "Newtonian Limits of Isolated Cosmological Systems on Long Time Scales"

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Cited by in corpus (15)

• Stabilizing relativistic fluids on spacetimes with non-accelerated expansion
• Cosmological Newtonian limits on large spacetime scales
• Future global stability for relativistic perfect fluids with linear equations of state $p=K\rho$ where $1/3<K<1/2$
• Future stability of the FLRW spacetime for a large class of perfect fluids
• Recent developments in mathematical aspects of relativistic fluids
• 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 instability of FLRW fluid solutions for linear equations of state $p=K\rho$ with $1/3<K<1$
• Localized big bang stability for the Einstein-scalar field equations
• Past instability of FLRW solutions of the Einstein-Euler-scalar field equations for linear equations of state $p=K\rho$ with $0\le K<1/3$
• Stability of AVTD Behavior within the Polarized $T^2$-symmetric vacuum spacetimes
• Rigorous proof of slightly nonlinear Jeans instability in the expanding Newtonian universe
• Stability of Asymptotic Behavior Within Polarised $T^2$-Symmetric Vacuum Solutions with Cosmological Constant
• Blowups for a class of second order nonlinear hyperbolic equations: A reduced model of nonlinear Jeans instability
• Blowups and longtime developments with near-boundary mass accretions of irregularly-shaped Euler--Poisson dominated molecular clouds in astrophysics