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Cosmological Newtonian limits on large spacetime scales. (English) Zbl 1402.83116
Summary: 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.

##### MSC:
 83F05 Relativistic cosmology 53Z05 Applications of differential geometry to physics 83C25 Approximation procedures, weak fields in general relativity and gravitational theory 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
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