Studies in Numerical Cosmology

*9800103 Berger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，爱因斯坦的方程式允许更大类别的宇宙学解。最初源于彭罗斯和霍金的定理预测，所有这样的模型(假设合理的物质性质)都会有一个初始奇点。一般宇宙学中这种奇点的性质在广义相对论中仍然是一个重大的悬而未决的问题。空间均匀但可能各向异性的宇宙有两种奇点：(1)速度主导型--(与时间方向相反)宇宙演化到具有固定各向异性塌缩速率的奇点；(2)Mixmaster--各向异性塌缩速率以确定的混沌方式变化。关于空间不均匀的宇宙，人们知之甚少。Belinskii、Khalatnikov和Lifshitz(BKL)很久以前就声称，一般宇宙将在每个空间点向奇点演化为不同的混合宇宙。这一长期研究计划将从数字上检验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.***