Newtonian Limits of Isolated Cosmological Systems on Long Time Scales

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= ϵ²Kρ, 0 < K≤ 1 / 3 , for the parameter values 0 < ϵ< ϵ₀. These solutions exist globally to the future, converge as ϵ↘ 0 to solutions of the cosmological Poisson–Euler equations of Newtonian gravity, and are inhomogeneous nonlinear perturbations of FLRW fluid solutions.