Cosmological Newtonian limits on large spacetime 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 on the manifold $M=(0,1]\times {\mathbb{R}}^3$, are future complete, and converge as $\epsilon \searrow 0$ to solutions of the cosmological Poisson-Euler equations. They represent inhomogeneous, nonlinear perturbations of a FLRW fluid solution where the inhomogeneities are driven by localized matter fluctuations that evolve to good approximation according to Newtonian gravity.

arXiv comment74 pages. Agrees with published version. arXiv admin note: text overlap with arXiv:1701.03975

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Cited by in corpus (14)

• Stabilizing relativistic fluids on spacetimes with non-accelerated expansion
• 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