ABSTRACT
In section 5.2, we looked at the physically well motivated model space-time for the universe. The metric of this space-time has only one function of time, the scale factor and its evolution reveals the first instance of a space-time singularity. Is this an artifact of the presumed very high degree of symmetry? Apart from the fact that the universe is certainly neither exactly homogeneous nor isotropic, the added interest in more general ‘cosmological spacetimes’ is for reasons of the issue of singularity. An obvious strategy would be to loosen the degree of symmetry required of the space-time. Thus as a first step, we give up isotropy, but retain homogeneity to get the class of homogeneous models. The next steps are to introduce inhomogeneities in just one direction to get for instance, the class of Gowdy models and finally to drop homogeneity completely. These mathematically motivated models also serve as testing ground for quantum versions of general relativity. In this chapter, we will discuss the class of homogeneous space-times and briefly describe the Belinskii-Khalatnikov-Lifshitz (BKL) conjecture for approach to a singularity.
