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 \({p = c^2_s \rho}\) , \({0 < c^2_s < 1/3}\) , the background solutions are globally future-stable. In particular, we prove that the perturbed spacetime solutions, which have the topological structure \({[0,\infty) \times \mathbb{T}^3}\) , 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.
Submitted Version (
Free)
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call