Although the observations appear to be well fitted by perturbed FLRW models, as described above, more general models need to be considered. One major reason is that the appropriateness of the perturbed FLRW models cannot be said to have been tested unless the consequences of alternatives have been calculated and compared with observation. In particular, there could be drastic changes to the models for the very early universe, since what may now be small and decaying perturbations in the standard picture would have been non-negligible earlier, and could give very different dynamics. Local observations can bound, but could not be sure to detect, such perturbations, so their testable consequences, if any, must arise from effects in the early universe.
We also need to consider the possibility of large-scale anisotropies, for example arising from a cosmic magnetic field aligned on a supergalactic scale, and of large-scale inhomogeneities (advanced as a possible explanation, which we discussed in Chapter 15, of the apparent acceleration seen in the supernova data).
This chapter considers the space of all models and the definition of classes of cosmological models wider than the FLRW models (compare e.g. Ellis (2005)). There are many ways of classifying spacetimes, of which the most common are by symmetry and by Petrov type (see Stephani et al. (2003)). In the cosmological case, symmetries are the more relevant and we consider that here. (Some models characterized by other covariant properties are described in Sections 19.6 and 19.7.)