angular momentum must play a strong role. Moreover, because of the elusiveness of dark matter, we know that the first two factors, applied just to visible material, cannot tell the whole story.

Consider, for instance, the density distribution of a cluster of galaxies. Like a sprawling metropolis, it has a greater concentration of galaxies packed within its central district than it does strewn way out in its suburbs. Hence, at least for visible material, clusters exhibit a density pattern that peaks at its center and drops off with radial distance. Superclusters display similar arrangements among the distribution of their member galaxies. They contain, however, several individual clusters and smaller groups of galaxies. Also, they may not be in equilibrium, meaning their forms are not settled.

Links between density distributions at various scales suggest that relative mass has more meaning than absolute mass in describing the state of the cosmos. After all, absolute mass is but a human invention. When we stand on a scale, we are comparing our bulk to a particular fixed amount. In metric units that standard is one kilogram—originally defined as the mass of a special platinum-iridium cylinder protected in an underground vault in Paris. Surely, galaxies don’t stop off in Paris when deciding how to arrange themselves.

Strange as it may seem, by temporarily abolishing the kilogram (and all other mass units) the theory frees up to have no particular scale. Instead, relative mass can be defined as a function of two fundamental quantities—the gravitational constant and the speed of light—as well as of the size of a particular region. This combination of distinct parameters could be an important clue to solving the mystery of why the naturally occurring laws of galaxy distribution comprise but a small subset among all possible arrangements. With these special assumptions in mind, we can construct self-similar cosmological solutions of Einstein’s equations that could represent the scale-free organization of material in the universe. By matching them up with the distributions of galaxies in clusters and superclusters, we could explain commonalities between those two scales.



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