2021A&A...647A..17E

Aims. We investigate the evolution of superclusters and supercluster cocoons (basins of attraction), and the effect of cosmological parameters on the evolution.
Methods. We performed numerical simulations of the evolution of the cosmic web for different cosmological models: the Λ cold dark matter (LCDM) model with a conventional value of the dark energy (DE) density, the open model OCDM with no DE, the standard SCDM model with no DE, and the hyper-DE HCDM model with an enhanced DE density value. We find ensembles of superclusters of these models for five evolutionary stages, corresponding to the present epoch z=0, and to redshifts z=1, 3, 10, and 30. We used the diameters of the largest superclusters and the number of superclusters as percolation functions to describe the properties of the ensemble of superclusters in the cosmic web. We analysed the size and mass distribution of superclusters in models and in real samples based on the Sloan Digital Sky Survey.
Results. In all models, the numbers and volumes of supercluster cocoons are independent of the cosmological epochs. The supercluster masses increase with time and the geometrical sizes in comoving coordinates decrease with time for all models. The LCDM, OCDM, and HCDM models have almost similar percolation parameters. This suggests that the essential parameter, which defines the evolution of superclusters, is the matter density. The DE density affects the growth of the amplitude of density perturbations and the growth of masses of superclusters, but significantly weaker. The HCDM model has the highest speed of the growth of the density fluctuation amplitude and the largest growth of supercluster masses during the evolution. The geometrical diameters and the numbers of HCDM superclusters at high threshold densities are larger than for the LCDM and OCDM superclusters. The SCDM model has about twice as many superclusters as other models, and the SCDM superclusters have smaller diameters and lower masses.
Conclusions. We find that supercluster embryos form at very early cosmological epochs and that the evolution of superclusters occurs mainly inside their cocoons. The evolution of superclusters and their cocoons as derived from density fields agress well with the evolution found from velocity fields.