On the isotropy of the Universe: do Bianchi cosmologies isotropize?

We study isotropization of the Universe by examining the evolution of a class of exact anisotropic cosmological solutions of Einstein's equations, namely spatially homogeneous cosmologies of Bianchi type with dust or radiation as the source. By using expansion-normalized variables, which unlike the usual metric variables are bounded throughout the evolution, we are able to give complete numerical simulations of the models, from the Planck time to the far-distant future. We find that two types of intermediate isotropization, characterized by the shear being small relative to the rate of expansion, can occur in Bianchi cosmologies, leading to models which are potentially compatible with the highly isotropic cosmic microwave background observations. In the first type the density parameter is close to one, while in the second type, it is not necessarily close to one. We relate these results to discussions by Doroshkevich et al and by Barrow of how isotropization occurs in cosmology.