Supercluster sample from SDSS DR4

We find for all supercluster samples Density Field (DF) clusters, which represent high-density peaks of the class of Abell clusters, and use median luminosities of richness class 1 DF-clusters to calculate relative luminosity functions.

We show that the fraction of very luminous superclusters in real samples is about five times greater than in simulated samples. Superclusters are generated by large-scale density perturbations that evolve very slowly. The absence of very luminous superclusters in simulations can be explained either by incorrect treatment of large-scale perturbations, or by some yet unknown processes in the very early Universe.