Liouville's theorem and the velocity field of galaxies

Did the large-scale distribution of matter in the Universe evolve by a dissipationless process (such as hierarchical clustering) or is it the result of a strongly dissipative event (such as the ‘pancake’ scenario)? If the distribution of galaxies in the Universe can be treated as a dissipationless fluid, then an application of Liouville's theorem predicts a linear relationship between the observed galaxy density and the cube of the velocity dispersion as measured at any point in space. Evidence from existing cluster data is presented here which supports this hypothesis.