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

In this article, we study small perturbations of the family of Friedmann-Lemâıtre-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 = csρ, 0 < cs < 1/3, the background solutions are globally future-stable. In particular, we prove that the perturbed spacetime solutions, which have the topological structure [0,∞)×T3, 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. Table of