在T^3-Gowdy对称Einstein-Vlasov背景下宇宙无毛猜想的证明
Proof of the cosmic no-hair conjecture in the T^3-Gowdy symmetric Einstein-Vlasov setting
摘要：
目前较受欢迎的宇宙模型经历了由暗能量引起的加速膨胀。暗能量的一个模型是正的宇宙学常数。因此，它是感兴趣的研究爱因斯坦方程与积极的宇宙学常数耦合到满足普通能量条件的物质;占主导地位的能量条件等由于难以分析的行为的解决方案，爱因斯坦方程一般，这是常见的研究情况与对称性，或证明稳定的结果。在本文中，我们两个都做。实际上，我们详细分析了具有正宇宙学常数的爱因斯坦-弗拉索夫方程的T^3-Gowdy对称解的未来渐近行为。特别是，我们证明了宇宙无毛猜想在这种情况下。然而，我们也证明了解决方案是未来稳定的（在类的所有解决方案）。一些结果在更一般的环境中也成立。事实上，我们得到了关于T^2对称解的因果结构的结论，只假设存在正的宇宙学常数，物质满足各种能量条件和未来的整体存在。在这个要求列表中加上T^3-Gowdy对称性的假设，我们得到了除了一个度量分量之外的所有度量分量的C^0-估计。因此，有理由期望本文中提出的许多结果可以推广到其他类型的物质。
英文摘要：
The currently preferred models of the universe undergo accelerated expansion induced by dark energy. One model for dark energy is a positive cosmological constant. It is consequently of interest to study Einstein's equations with a positive cosmological constant coupled to matter satisfying the ordinary energy conditions; the dominant energy condition etc. Due to the difficulty of analysing the behaviour of solutions to Einstein's equations in general, it is common to either study situations with symmetry, or to prove stability results. In the present paper, we do both. In fact, we analyse, in detail, the future asymptotic behaviour of T^3-Gowdy symmetric solutions to the Einstein-Vlasov equations with a positive cosmological constant. In particular, we prove the cosmic no-hair conjecture in this setting. However, we also prove that the solutions are future stable (in the class of all solutions). Some of the results hold in a more general setting. In fact, we obtain conclusions concerning the causal structure of T^2-symmetric solutions, assuming only the presence of a positive cosmological constant, matter satisfying various energy conditions and future global existence. Adding the assumption of T^3-Gowdy symmetry to this list of requirements, we obtain C^0-estimates for all but one of the metric components. There is consequently reason to expect that many of the results presented in this paper can be generalised to other types of matter.
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