Structure of the Universe in the two-dimensional model of adhesion

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Abstract
We discuss a model for the formation of the Large-Scale Structure in the Universe dominated by dark matter. The model approximately describing the non-linear stage of gravitational instability is based on the Burgers equation (adhesion or sticking model). Contrary to the widely accepted practice of using the linear density perturbations for the analysis of the structure formation, we describe the initial conditions in terms of the gravitational potential perturbations at the linear stage φ(r). The skeleton of the mass distribution at an arbitrary time t is calculated directly without intermediate steps and with the aid of the geometrical technique of constructing paraboloids tangential to the hypersurface φ(r). The curvature of the paraboloid depends on time only. Decreasing with time it results in evolution of the skeleton of the mass distribution. Here we compare this model with the direct N-body simulations in two dimensions. The suggested model is shown to be in satisfactory qualitative agreement with results of the N-body simulation. Our results confirm the potential merits of the adhesion model for a wide class of cosmological scenarios including the Cold Dark Matter model.

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