The 'fitting problem' in cosmology

This paper considers the best way to fit an idealised exactly homogeneous and isotropic universe model to a realistic ('lumpy') universe; whether made explicit or not, some such approach of necessity underlies the use of the standard Robertson-Walker models as models of the real universe. Approaches based on averaging, normal coordinates and null data are presented, the latter offering the best opportunity to relate the fitting procedure to date obtainable by astronomical observations.