## Abstract

In this article, we study small perturbations of the family of Friedmann-Lemaǐtre-Robertson-Walker cosmological background solutions to the coupled Euler-Einstein system with a positive cosmological constant in 1 + 3 spacetime dimensions. The background solutions model an initially uniform quiet fluid of positive energy density evolving in a spacetime undergoing exponentially accelerated expansion. Our nonlinear analysis shows that under the equation of state p = c^{2}_{s} ρ, 0 < c_{s} < √1/3, the background metric + fluid solutions are globally future-stable under small irrotational perturbations of their initial data. In particular, we prove that the perturbed spacetime solutions, which have the topological structure [0, ∞) × T^{3}, are future causally geodesi-cally complete. Our analysis is based on a combination of energy estimates and pointwise decay estimates for quasilinear wave equations featuring dissipative inhomogeneous terms. Our main new contribution is showing that when 0 < c_{s} < √1/3, exponential spacetime expansion is strong enough to suppress the formation of fluid shocks. This contrasts against a well-known result of Christodoulou, who showed that in Minkowski spacetime, the corresponding constant-state irrotational fluid solutions are unstable.

Original language | English (US) |
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Pages (from-to) | 2369-2462 |

Number of pages | 94 |

Journal | Journal of the European Mathematical Society |

Volume | 15 |

Issue number | 6 |

DOIs | |

State | Published - 2013 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

## Keywords

- Cosmological constant
- Energy dissipation
- Expanding spacetime
- Geodesically complete
- Global existence
- Irrotational fluid
- Relativistic fluid
- Wave coordinates