The Stability of the Irrotational Euler-Einstein System with a Positive Cosmological Constant

Details The Stability of the Irrotational Euler-Einstein System with a Positive Cosmological Constant The Stability of the Irrotational Euler-Einstein System with a Positive Cosmological Constant

2009-11-29

arxiv.org/abs/0911.5501v2

Physics

Mathematical Physics

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Scientific paper

In this article, we study small perturbations of the family of Friedmann-Lema\^itre-Robertson-Walker cosmological background solutions to the Euler-Einstein system with a positive cosmological constant in 1 + 3 dimensions. The background solutions describe an initially uniform quiet fluid of positive energy density evolving in a spacetime undergoing accelerated expansion. We show that under the equation of state p = c_s^2*(energy density), 0 < c_s^2 < 1/3, the background solutions are globally future asymptotically stable under small irrotational perturbations. In particular, we prove that the perturbed spacetimes, which have the topological structure [0,infinity) x T^3, are future causally geodesically complete.

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