Cosmological Newtonian limits on large spacetime scales

Abstract

We establish the existence of $1$-parameter families of $ε$-dependent solutions to the Einstein-Euler equations with a positive cosmological constant $Λ>0$ and a linear equation of state $p=ε^2 K ρ$, $0<K\leq 1/3$, for the parameter values $0<ε< ε_0$. These solutions exist globally on the manifold $M=(0,1]\times \mathbb{R}^3$, are future complete, and converge as $ε\searrow 0$ 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.

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