Evolution of the supercluster-void network.

Recently, the observed cellular nature of the large-scale structure of the Universe with its quasi-regular pattern of superclusters and voids has been pointed out by several authors. In this paper, we investigate properties of the initial power spectrum which lead to prediction of structure consistent with these observations. For this purpose, we analyze the evolution of structure within four sets of 2- and 3-dimensional cosmological models, which differ in their initial power spectrum. The models include HDM and CDM models as well as double power-law models. We discuss in detail the impact of model parameters such as the large scale and small scale power and the position and height of the maxima of the power spectra on the predicted structure. Several statistical techniques were employed to compare the models with observations. They include the analysis of the distribution of voids defined by rich and poor clusters of galaxies, voids defined by galaxies, clusters and superclusters. In addition, the cluster correlation function is compared. We conclude that the observed regular distribution of superclusters and voids can be reproduced only if the spectrum of density fluctuations has a well-defined maximum. The wavelength of the maximum determines the scale of the structure. Small-scale fluctuations determine the fine structure of the Universe. Large-scale fluctuations modulate the fine structure and determine the quasi-regular structure on supercluster scales. The best agreement with observations was observed in the model with the Harrison-Zeldovich spectrum on large scales, a power index n=~-1.5 on small scales, and a maximum of the power spectrum at =~130h^-1^Mpc. In this model the distribution of masses of clusters and superclusters, the correlation function of clusters, and the void distribution reproduce well the respective observed distributions. In models with no power on large scales all superclusters are equal in mean density, while in models with negative power index on large scales the mass distribution function of clusters is too shallow. In the HDM model (no power on small scales) the cluster-defined voids are completely empty. CDM-models have no well-defined maximum of the spectrum, and the cellular distribution of superclusters and voids is insufficiently developed in this case. We also investigated the dynamical evolution of the super- cluster-void structure. The results show that the basic super- cluster-void network is formed very early and is essentially given by initial conditions.