The dynamical parameters of the expanding universe as they constrain homogeneous world models with and without Λ

On scales larger than --300 Mpc (i.e. over regions separated by expansion velocities of at least 15,000 km s/sup -1/), the Universe is observed to be homogeneous; the mean density averaged over volumes of this size is much the same from cell to cell no matter which cell is considered. As the scale is decreased, structure begins to appear, and at --100 Mpc (v--5000 km s/sup -1/) superclusters appear whose form is either pancakes or simple strings of galaxies connecting the cores of dense clusters. On scales of --20 Mpc the principal structures are the dense envelopes surrounding the cluster cores such as that of our own Virgo-complex supercluster. Between the scale at --100 Mpc and this scale at --20 Mpc, voids appear. On still smaller scales of --2 Mpc, the cores of the clusters are the principal structures, appearing at the intersections of the supercluster pancakes. These are to be identified with the clusters. Smaller groups of galaxies exist with higher frequency, also at this scale. The Local Group is the best known example. The greatest density fluctuations on the smallest scale are the galaxies themselves, with typical scale-lengths of --0.1 Mpc for the largest, ranging down to at least one hundredth of that