Abundances and Correlations of Structures Beyond Galaxy Clusters

We investigated the structures on scales beyond the typical clusters of galaxies. These structures are crucial to understand the cosmic gravitational clustering in the pre-virialized stage, or quasilinear r\`egime. Based on the multi-resolution analysis of the discrete wavelet transformation, we got statistical available ensembles of $r_{cl}$-clusters, i.e. the structures on scale $r_{cl}$, in the range $1 \leq r_{cl} \leq 24 h^{-1}$ Mpc for both N-body simulation and the IRAS 1.2 Jy galaxy survey samples. If the mass-to-light ratio on scales larger than clusters asymptotically reaches a constant, we found that the abundances and correlations of these IRAS $r_{cl}$-clusters to be basically consistent with the predictions of the flat low-density CDM model (LCDM) and the open CDM model (OCDM), except the model-predicted abundance of $r_{cl} = 24 h^{-1}$ Mpc clusters seems to be higher than IRAS data. The standard CDM (SCDM) gives too much power, and too weak correlations on all the scales. For a given $r_{cl}$, the amplitude of two-point correlation function of $r_{cl}$-clusters is increasing with their richness. However, for a given richness (defined by the mean separation of neighbor objects), the clustering strengths of both simulation and observation sample are found to be declining with $r_{cl}$ when $r_{cl}$ is larger than 3 - 4 $h^{-1}$ Mpc. Therefore, the ``universal'' increase of the correlation amplitude with the scale of objects from galaxies, groups, to poor, rich clusters is broken down for structures of $r_{cl} > 3 - 4 h^{-1}$ Mpc. Supercluster should not be a member of the ``universal'' increase family.