We establish the existence of 1-parameter families of $$\epsilon $$ ϵ -dependent solutions to the Einstein–Euler equations with a positive cosmological constant $$\Lambda >0$$ Λ > 0 and a linear equation of state $$p=\epsilon ^2 K \rho $$ p = ϵ 2 K ρ , $$0<K\le 1/3$$ 0 < K ≤ 1 / 3 , for the parameter values $$0<\epsilon < \epsilon _0$$ 0 < ϵ < ϵ 0 . These solutions exist globally to the future, converge as $$\epsilon \searrow 0$$ ϵ ↘ 0 to solutions of the cosmological Poisson–Euler equations of Newtonian gravity, and are inhomogeneous nonlinear perturbations of FLRW fluid solutions.
Annales Henri Poincaré – Springer Journals
Published: Jun 4, 2018
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