Newtonian Limits of Isolated Cosmological Systems on Long Time Scales

Abstract

We establish the existence of $1$-parameter families of $\hat{I}\mu$-dependent solutions to the Einstein-Euler equations with a positive cosmological constant $\hat{I}›>0$ and a linear equation of state $p=\hat{I}{\mu }^{2}K\ddot{I}$, $0<K\le 1/3$, for the parameter values $0<\hat{I}\mu <\hat{I}{\mu }_0$. These solutions exist globally to the future, converge as $\hat{I}\mu \searrow 0$ 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"