Shear-free anisotropic cosmological models

A class of orthogonal, spatially homogeneous shear-free cosmological models with an imperfect liquid matter content is considered. It is shown that, for these models, the anisotropic stresses are related to the anisotropic curvature of the spatial hypersurfaces through the electric part of the Weyl tensor. This creates a counterbalance effect which has important consequences for the evolution of the cosmological models. Such features are discussed, and, as an application, some eternally anisotropic models with an imperfect fluid stress tensor which exhibit FRW-like behaviour are given.