The sponge-like topology of large-scale structure in the universe

Abstract

We describe and apply a quantitative measure of the topology of large scale structure: the genus of density contours in a smoothed density distribution. For random phase (gaussian) density fields, the mean genus per unit volume exhibits a universal dependence on threshold density, with a normalizing factor that can be calculated from the power spectrum. The topology of the observational sample is consistent with the random phase, cold dark matter model.