具有正宇宙学常数的无旋Euler-Einstein系统的稳定性
The Stability of the Irrotational Euler-Einstein System with a Positive Cosmological Constant
摘要：
本文研究了1 + 3维中具有正宇宙学常数的Euler-Einstein系统的Friedmann-Lemaitre-Robertson-Walker宇宙学背景解族的小扰动.背景解描述了一个初始均匀的正能量密度的安静流体在经历加速膨胀的时空中演化。我们证明了在状态方程p = c_s^2*（能量密度），0 < c_s^2 < 1/3下，背景解在小的无旋扰动下是全局未来渐近稳定的.特别地，我们证明了具有拓扑结构[0，无穷大）× T^3的扰动时空是未来因果测地线完备的。
英文摘要：
In this article, we study small perturbations of the family of Friedmann-Lemaître-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.
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