  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 to the future, converge as $\epsilon \searrow 0$ to solutions of the
cosmological Poison-Euler equations of Newtonian gravity, and are inhomogeneous
non-linear perturbations of FLRW fluid solutions.
