Galaxies and clusters of galaxies are complex systems, but the aim of the cosmologist is not to explain all their detailed features. Rather, it is to explain howlarge-scale structures formed in the expanding Universe in the sense that, if δρ is the enhancement in density of some region over the average background density ρ, the density contrast δρ/ρ reached amplitude 1 from initial conditions which must have been remarkably isotropic and homogeneous. Once the initial perturbations have grown in amplitude to δρ/ρ ~ 1, their growth becomes non-linear and they rapidly evolve towards bound structures in which star formation and other astrophysical process lead to the formation of galaxies and clusters of galaxies as we know them. The cosmologist's objectives are therefore twofold – to understand how density perturbations evolve in the expanding Universe and to derive the initial conditions necessary for the formation of structure in the Universe.
Galaxies, clusters of galaxies and other large-scale structures of our local Universe must have formed relatively late in the history of the Universe. The average density of matter in the Universe today corresponds to a density parameter Ω 0 ~ 0. 3. The average densities of gravitationally bound systems, such as galaxies and clusters of galaxies, are much greater than this value, typically their densities being about 106 and 1000 times greater than the mean background density, respectively. Superclusters have mean densities a few times the background density.