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arXiv · 1102.1501

The Nonlinear Future-Stability of the FLRW Family of Solutions to the Euler-Einstein System with a Positive Cosmological Constant

Jared Speck
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Abstract

In this article, we study small perturbations of the family of Friedmann-Lemaître-Robertson-Walker cosmological background solutions to the 1 + 3 dimensional Euler-Einstein system with a positive cosmological constant. These background solutions describe an initially uniform quiet fluid of positive energy density evolving in a spacetime undergoing accelerated expansion. Our nonlinear analysis shows that under the equation of state pressure = c_s^2 * energy density, with 0 < c_s^2 < 1/3, the background solutions are globally future-stable. In particular, we prove that the perturbed spacetime solutions, which have the topological structure [0,infty) x T^3, are future causally geodesically complete. These results are extensions of previous results derived by the author in a collaboration with I. Rodnianski, in which the fluid was assumed to be irrotational. Our novel analysis of a fluid with non-zero vorticity is based on the use of suitably-defined energy currents.

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Jared Speck. 2012-01-24. The Nonlinear Future-Stability of the FLRW Family of Solutions to the Euler-Einstein System with a Positive Cosmological Constant. https://arxiv.org/abs/1102.1501

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