Berger The 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. ***