TOWARDS THEORETICAL MODELLING OF DISTRIBUTION OF MATTER IN UNIVERSE

Abstract

The description of the distribution of matter in the universe requires not only accurate observations but also adequate approaches to their theoretical interpretation. This paper proposes a method of parameterization of distributions with a morphologically complex topology using structural invariants (for example, Euler), based on which it is possible to distinguish clusters with different topologies (in the observation plane). Based on the introduced classification and appropriate scaling, it becomes possible to estimate the distribution of matter, for example, within the framework of the mean-field model. To study the kinetics of the evolution of matter distribution, it is proposed to introduce the appropriate ordering parameter, which is built based on the calibrating and current values of the Euler-Poincaré invariants. This approach, by constructing phase diagrams for the ordering parameter, allows you to track the details of the kinetics of the evolution of matter distributions, studying, in particular, the temporal hierarchy of relaxation times of intermediate states. The temporal kinetics of this approach are described using simple kinetic equations that describe the relaxation of the ordering parameter field, and the values of invariants determined with the help of appropriate measurements (observations) appear as initial conditions. This approach can be seen as an alternative to other approaches to parameterization of structurally complex systems, such as Voronoi methods, graphs, etc. A comparative analysis of the results of various alternative approaches to the parameterization of topologically complex distributions of matter, which will be conducted in the future, should contribute to the deepening of existing ideas about the nature of the distribution of matter in the Universe.