Evolution of superclusters in the cosmic web

Aims. We investigate how properties of the ensemble of superclusters in the cosmic web evolve with time. Methods. We performed numerical simulations of the evolution of the cosmic web using the Lambda cold dark matter model in box sizes L-0 = 1024; 512; 256 h(-1) Mpc. We found supercluster ensembles of models for four evolutionary stages, corresponding to the present epoch z = 0, and to redshifts z = 1, z = 3, and z = 10. We calculated fitness diameters of superclusters defined from volumes of superclusters divided by filling factors of over-density regions. Geometrical and fitness diameters of largest superclusters, and the number of superclusters as functions of the threshold density were used as percolation functions to describe geometrical properties of the ensemble of superclusters in the cosmic web. We calculated the distributions of geometrical and fitness diameters and luminosities of superclusters, and followed the time evolution of percolation functions and supercluster distributions. We compared percolation functions and supercluster distributions of models and samples of galaxies of the Sloan Digital Sky Survey (SDSS). Results. Our analysis shows that fitness diameters of superclusters have a minimum at a certain threshold density. Fitness diameters around minima almost do not change with time in co-moving coordinates. Numbers of superclusters have maxima which are approximately constant for all evolutionary epochs. The geometrical diameters of superclusters decrease during the evolution of the cosmic web, and the luminosities of superclusters increase during this evolution. Conclusions. Our study suggests that evolutionary changes occur inside supercluster cells of dynamical influence. The stability of fitness diameters and numbers of superclusters during the evolution is an important property of the cosmic web.