Cosmological aspects of hydrodynamic treatment of the Einstein–Vlasov equations

The principle of the least action and the Vlasov kinetic formalism is used to derive the closed set of equations defining the systems of gravitating particles. The hydrodynamic approximation is shown to enable one to reduce the Vlasov equation to the Euler–Courant equations, including in the Hamilton–Jacobi form. Exact solutions of those equations for non-relativistic cosmological models of Milne–McCrea form with Gurzadyan’s potential are obtained, which, particularly, enables to address the Hubble tension problem.