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首页> 外文期刊>Journal of the European Mathematical Society: JEMS >The nonlinear future stability of the FLRW family of solutions to the irrotational Euler-Einstein system with a positive cosmological constant
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The nonlinear future stability of the FLRW family of solutions to the irrotational Euler-Einstein system with a positive cosmological constant

机译：具有正宇宙学常数的无旋Euler-Einstein系统FLRW系列解的非线性未来稳定性

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摘要

In this article, we study small perturbations of the family of Friedmann-Lema?tre- Robertson-Walker cosmological background solutions to the coupled Euler-Einstein system with a positive cosmological constant in 1 + 3 spacetime dimensions. The background solutions model an initially uniform quiet fluid of positive energy density evolving in a spacetime undergoing exponentially accelerated expansion. Our nonlinear analysis shows that under the equation of state p = c_s~2 p, 0 < c_s < 1/3~(1/2), the background metric + fluid solutions are globally future-stable under small irrotational perturbations of their initial data. In particular, we prove that the perturbed spacetime solutions, which have the topological structure [0, ∞)×T~3; are future causally geodesically complete. Our analysis is based on a combination of energy estimates and pointwise decay estimates for quasilinear wave equations featuring dissipative inhomogeneous terms. Our main new contribution is showing that when 0 < c_s < 1/3~(1/2), exponential spacetime expansion is strong enough to suppress the formation of fluid shocks. This contrasts against a well-known result of Christodoulou, who showed that in Minkowski spacetime, the corresponding constant-state irrotational fluid solutions are unstable.
机译：在本文中，我们研究了耦合的Euler-Einstein系统的Friedman-Lema？tre-Robertson-Walker宇宙学背景解家族的小扰动，在1 + 3时空维度中具有正的宇宙常数。背景解决方案对正能量密度的初始均匀安静流体进行建模，该流体在时空中经历指数加速膨胀。我们的非线性分析表明，在状态方程p = c_s〜2 p，0

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