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.

Preprint

Comment: 7 pages, 1 fig., A&A (in press)

Subject: Astrophysics - Cosmology and Nongalactic Astrophysics