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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 on the manifold M= (0 , 1 ] × R3, are future complete, and converge as ϵ↘ 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.
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