### Abstract

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= ϵ^{2}Kρ, 0 < K≤ 1 / 3 , for the parameter values 0 < ϵ< ϵ_{0}. These solutions exist globally on the manifold M= (0 , 1 ] × R^{3}, 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.

Original language | English |
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Pages (from-to) | 1195-1304 |

Number of pages | 110 |

Journal | Communications in Mathematical Physics |

Volume | 364 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Dec 2018 |

## Cite this

Liu, C., & Oliynyk, T. (2018). Cosmological Newtonian Limits on Large Spacetime Scales.

*Communications in Mathematical Physics*,*364*(3), 1195-1304. https://doi.org/10.1007/s00220-018-3214-9