The Stability of the Irrotational Euler-Einstein System with a Positive Cosmological Constant

Understand

In this article, we study small perturbations of the family of Friedmann-Lema\^itre-Robertson-Walker cosmological background solutions to the Euler-Einstein system with a positive cosmological constant in 1 + 3 dimensions.

• The background solutions describe an initially uniform quiet fluid of positive energy density evolving in a spacetime undergoing accelerated expansion.
• We show that under the equation of state p = c_s^2*(energy density), 0 < c_s^2 < 1/3, the background solutions are globally future asymptotically stable under small irrotational perturbations.
• In particular, we prove that the perturbed spacetimes, which have the topological structure [0,infinity) x T^3, are future causally geodesically complete.