### Abstract

We prove the existence of a large class of one parameter families of solutions to the Einstein-Euler equations that depend on the singular parameter \epsilon=v_T/c (0<\epsilon <\epsilon_0) , where c is the speed of light, and v T is a typical speed of the gravitating fluid. These solutions are shown to exist on a common spacetime slab M\cong [0,T)\times \mathbb T ^3 , and converge as \epsilon \searrow 0 to a solution of the cosmological Poisson-Euler equations of Newtonian gravity. Moreover, we establish that these solutions can be expanded in the parameter \epsilon to any specified order with expansion coefficients that satisfy \epsilon -independent (nonlocal) symmetric hyperbolic equations.

Original language | English |
---|---|

Pages (from-to) | 431 - 463 |

Number of pages | 33 |

Journal | Communications in Mathematical Physics |

Volume | 295 |

Issue number | 2 |

Publication status | Published - 2010 |

## Cite this

Oliynyk, T. A. (2010). Cosmological post-Newtonian expansions to arbitrary order.

*Communications in Mathematical Physics*,*295*(2), 431 - 463.