  In this article, we study small perturbations of the family of
Friedmann-Lema\^itre-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.
