Studies in Numerical Cosmology

* 9800103伯格空间均匀、各向同性的标准宇宙学模型似乎可以很好地描述我们的宇宙。 然而，爱因斯坦方程允许更大类的宇宙学解。 最初由彭罗斯和霍金提出的定理预言，所有这样的模型（假设合理的物质性质）都将有一个初始奇点。 在广义宇宙学中，这种奇点的性质仍然是广义相对论中一个主要的悬而未决的问题。 空间均匀但可能各向异性的宇宙学有两种类型的奇点：（1）速度主导-（反转时间方向）宇宙以固定的各向异性坍缩率演化到奇点;（2）Mixmaster-各向异性坍缩率以确定性混沌的方式变化。 关于空间非均匀宇宙的了解要少得多，Belinskii，Khalatnikov和Lifshitz（BKL）很久以前就声称，一个普通宇宙将在每个空间点上作为一个不同的Mixmaster宇宙向奇点演化。 这个长期的研究计划将在数值上测试BKL猜想。

***9800103BergerThe spatially homogeneous, isotropic Standard Cosmological Model appears to describe our Universe reasonably well. However, Einstein's equations allow a much larger class of cosmological solutions. Theorems originally due to Penrose and Hawking predict that all such models (assuming reasonable matter properties) will have an initial singularity. The nature of this singularity in generic cosmologies remains a major open question in general relativity. Spatially homogeneous but possibly anisotropic cosmologies have two types of singularities: (1) velocity dominated--(reversing the time direction) the universe evolves to the singularity with fixed anisotropic collapse rates; (2) Mixmaster--the anisotropic collapse rates change in a deterministically chaotic way. Much less is known about spatially inhomogeneous universes.Belinskii, Khalatnikov, and Lifshitz (BKL) claimed long ago that a generic universe would evolve toward the singularity as a different Mixmaster universe at each spatial point. This long-term research program will test the BKL conjecture numerically.***