Cosmological Newtonian limits on large spacetime scales

We establish the existence of $1$-parameter families of $ϵ$-dependent solutions to the Einstein-Euler equations with a positive cosmological constant $\mathrm{\Lambda }>0$ and a linear equation of state $p={ϵ}^{2}K\rho$, $0<K\leq 1/3$,fortheparametervalues$0<\epsilon < \epsilon_0$. 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.