Morphology of the supercluster–void network in ΛCDM cosmology

We report here the first systematic study of the supercluster–void network in the ΛCDM concordance cosmology in which voids and superclusters are treated on an equal footing. We study the dark matter density field in real space smoothed on a scale of 5 h⁻¹ Mpc. Superclusters are defined as individual members of an overdense excursion set, and voids are defined as individual members of a complementary underdense excursion set at the same density threshold. We determine the geometric, topological and morphological properties of the cosmic web at a large set of density levels by computing Minkowski functionals for every supercluster and void using surfgen (described recently by Sheth et al.). The properties of the largest (percolating) supercluster and the complementary void are found to be very different from those of the individual superclusters and voids. In total, the individual superclusters occupy no more than about 5 per cent of the volume and contain no more than 20 per cent of the mass if the largest supercluster is excluded. Likewise, in total, individual voids occupy no more than 14 per cent of the volume and contain no more than 4 per cent of the mass if the largest void is excluded. Although superclusters are more massive and voids are more voluminous, the difference in maximum volumes is no greater than an order of magnitude. The genus value of individual superclusters can be ∼5, while the genus of individual voids can reach ∼50, implying a significant amount of substructure in superclusters and especially in voids. One of our main results is that large voids, as defined through the dark matter density field in real space, are distinctly non-spherical.