The nonlinear future stability of the FLRW family of solutions to the Euler–Einstein system with a positive cosmological constant
Author(s)Speck, Jared R.
MetadataShow full item record
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.
Original manuscript January 24, 2012
DepartmentMassachusetts Institute of Technology. Department of Mathematics
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.