The nonlinear future stability of the FLRW family of solutions to the Euler-Einstein system with a positive cosmological constant

• Main Author: Speck, Jared R. (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor), Speck, Jared (Contributor)
• Format: Article
• Language: English
• Published: Springer-Verlag, 2013-11-01T17:42:57Z.
• Subjects: Article
• Online Access: Get fulltext

Original manuscript January 24, 2012
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 p=c[2 over s]ρ, 0 < c[2 over s] < 1/3 , the background solutions are globally future-stable. In particular, we prove that the perturbed spacetime solutions, which have the topological structure [0,∞) × T[superscript 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.
National Science Foundation (U.S.). All-Institutes Postdoctoral Fellowship (Mathematical Sciences Research Institute (Berkeley, Calif.) Grant DMS-0441170)