Studies in Numerical Cosmology

伯格空间均匀、各向同性的标准宇宙学模型似乎相当好地描述了我们的宇宙。然而，爱因斯坦的方程允许一个更大的宇宙解类。最初由彭罗斯和霍金提出的定理预测，所有这些模型（假设合理的物质属性）都将有一个初始奇点。一般宇宙学中这种奇点的性质仍然是广义相对论中一个悬而未决的主要问题。空间均匀但可能各向异性的宇宙学有两种奇点：(1)速度占主导地位——（逆转时间方向）宇宙演化到具有固定的各向异性坍缩率的奇点；(2) Mixmaster——各向异性坍缩率以确定性混沌的方式变化。我们对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，一个通用宇宙将在每个空间点作为不同的Mixmaster宇宙向奇点演化。这项长期研究计划将在数值上验证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.***