Cosmological Aspects of the Theory of Equations of the Vlasov–Einstein Type and Their Consequences

Abstract

The authors propose a general scheme of derivation from the general relativistic Einstein-Hilbert action for a system of gravitationally interacting charged particles, Hamilton’s dynamics equations and field equations. In accordance with the proposed methodology, new forms of equations of Vlasov type are obtained in the general relativistic case, nonrelativistic and weakly relativistic limits. Expressions are established for the resulting corrections in the equation Poisson, which can contribute to the action of dark matter and dark energy. An effective approach to synchronizing the proper times of different particles of a many-particle system is proposed based on invariance of the form of action. Authors derived (using hydrodynamic substitution) and solved the Euler-type equations leading to the cosmological Friedmann and Milne-McCrea models.