Cosmic Voids and the Kinetic Analysis

The kinetic approach to the formation of the filaments in the large-scale matter distribution in the Universe is considered within the Vlasov formalism. The structures arise due to the self-consistent dynamics, along with the repulsive term in the modified Newtonian gravity which includes the cosmological constant. That modified gravity enables one to describe the Hubble tension as a result of two flows, the local and global ones. The criteria for formation of non-stationary semi-periodic structures in a system of gravitating particles described by Vlasov-Poisson equations are obtained in the case of that repulsive term. The obtained dispersion relations for the Vlasov equation in the vicinity of the singular point of the modified gravitational potential demonstrate the possibility of the emergence of filaments as coherent complex states of relative equilibrium in non-stationary systems as structures of low dimensions (walls), and voids between them, of scales (diameters) defined by the balance between the gravity and repulsive term of the cosmological constant.