The nonlinear future stability of the FLRW family of solutions to the Euler–Einstein system with a positive cosmological constant
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Speck_The nonlinear future.pdf
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897.51 KB
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Author(s)
Speck, Jared R.
Date Issued
April 2012
Journal
Selecta Mathematica
Publisher
Springer-Verlag
Citation
Speck, Jared. “The nonlinear future stability of the FLRW family of solutions to the Euler–Einstein system with a positive cosmological constant.” Selecta Mathematica 18, no. 3 (September 19, 2012): 633-715.
Version
Original manuscript
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 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.
Description
Original manuscript January 24, 2012
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1007/s00029-012-0090-6
