# Newtonian Limits of Isolated Cosmological Systems on Long Time Scales

Newtonian Limits of Isolated Cosmological Systems on Long Time Scales We establish the existence of 1-parameter families of $$\epsilon$$ ϵ -dependent solutions to the Einstein–Euler equations with a positive cosmological constant $$\Lambda >0$$ Λ > 0 and a linear equation of state $$p=\epsilon ^2 K \rho$$ p = ϵ 2 K ρ , $$0<K\le 1/3$$ 0 < K ≤ 1 / 3 , for the parameter values $$0<\epsilon < \epsilon _0$$ 0 < ϵ < ϵ 0 . These solutions exist globally to the future, converge as $$\epsilon \searrow 0$$ ϵ ↘ 0 to solutions of the cosmological Poisson–Euler equations of Newtonian gravity, and are inhomogeneous nonlinear perturbations of FLRW fluid solutions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annales Henri Poincaré Springer Journals

# Newtonian Limits of Isolated Cosmological Systems on Long Time Scales

, Volume 19 (7) – Jun 4, 2018
87 pages

/lp/springer_journal/newtonian-limits-of-isolated-cosmological-systems-on-long-time-scales-VdC9aVgaKq
Publisher
Springer Journals
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Physics; Theoretical, Mathematical and Computational Physics; Dynamical Systems and Ergodic Theory; Quantum Physics; Mathematical Methods in Physics; Classical and Quantum Gravitation, Relativity Theory; Elementary Particles, Quantum Field Theory
ISSN
1424-0637
eISSN
1424-0661
D.O.I.
10.1007/s00023-018-0686-2
Publisher site
See Article on Publisher Site

### Abstract

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

### Journal

Annales Henri PoincaréSpringer Journals

Published: Jun 4, 2018

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