Simulated evolution of the dark matter large-scale structure

We analyze evolution of the basic properties of simulated large scale structure elements formed by dark matter (DM LSS) and confront it with the observed evolution of the Lyman-$\alpha$ forest. In three high resolution simulations we selected samples of compact DM clouds of moderate overdensity. Clouds are selected at redshifts $0\leq z\leq 3$ with the Minimal Spanning Tree (MST) technique. The main properties of so selected clouds are analyzed in 3D space and with the core sampling approach, what allows us to compare estimates of the DM LSS evolution obtained with two different techniques and to clarify some important aspects of the LSS evolution. In both cases we find that regular redshift variations of the mean characteristics of the DM LSS are accompanied only by small variations of their PDFs, what indicates the self similar character of the DM LSS evolution. The high degree of relaxation of DM particles compressed within the LSS is found along the shortest principal axis of clouds. We see that the internal structure of selected clouds depends upon the mass resolution and scale of perturbations achieved in simulations. It is found that the low mass tail of the PDFs of the LSS characteristics depends upon the procedure of clouds selection.