The Charlier Universe

The universe may be spatially infinite, and contain an infinite amount of mass-energy, but the average density of mass-energy may be zero. This is the little-known conclusion of the Swedish astronomer, Carl Vilhelm Ludwig Charlier, who developed a 'hierarchical' cosmological model between 1908 and 1924. In such a model, there is no length-scale above which the distribution of mass-energy becomes homogeneous. There are galaxies, then clusters of galaxies, then superclusters, then super-superclusters, and so on, ad infinitum, with the density of mass-energy decreasing the further one goes up the hierarchy. As the level of the hierarchy tends to infinity, the density of mass-energy in that hierarchical level tends to zero.

The Charlier universe is inconsistent with the 'Big-Bang' cosmological models (i.e., the Friedmann-Robertson-Walker models), but is the Charlier universe nevertheless consistent with the observed astronomical distribution of mass-energy? Well, on length scales up to 100 mega-parsecs(Mpc), the universe exhibits large inhomogeneities and anisotropies. The distribution of matter is characterised by walls and filaments of galaxies, surrounding huge voids, and these clusters and superclusters of galaxies exhibit large 'peculiar' velocities relative to the cosmic microwave background radiation. Whilst most astronomers claim that the matter distribution becomes homogeneous above 100Mpc, this is a belief independent of observation because the distribution could clearly undergo another step-change on a length-scale above that to which the current generation of telescope is capable of reaching.