18 - Spatially homogeneous anisotropic models

Summary

FLRW models are spatially homogeneous, but they are a very restricted subclass of such models because of their isotropy. Why are spatially homogeneous anisotropic models interesting? Basically, because they are tractable solutions of the full non-linear equations since there is only one essential variable, time, so the equations become ordinary differential equations, but they allow investigation of much more general behaviour than the FLRW models. They can represent anisotropic modes, including rotation and global magnetic fields, which could occur in the real universe (indeed, must do so, if the universe is indeed generic, as some claim): here an anisotropic but not necessarily inhomogeneous model is required (see e.g. Thorne (1967)). They allow new classes of singularities, and modification of the BBN–baryon relation in the early universe. They may also be good approximations in regions where there is inhomogeneity but spatial gradients are small, see Section 19.9. They have been explored in various quantum cosmology contexts (see Chapter 20) as well as in GR.

In particular, the tilted cases provide the only tractable cosmological solutions we have which involve rotation: rotation is ubiquitous in the universe, and, because of the vorticity conservation theorems discussed in Chapter 6, this suggests there always was and always will be rotation. Thus it is valuable to have solutions where we can investigate its effects on, for example, the CMB, where we find new classes of anisotropy patterns, and on nucleosynthesis.