  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 $p=\epsilon^2 K \rho$, $0<K\leq
1/3$, 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.
