On derivation of Vlasov–Maxwell–Einstein equations from the principle of least action, the Hamilton–Jacobi method, and the Milne–Mccrea model

In classical texts equations for gravitation and electromagnetic fields are proposed without deriving their right-hand sides [1–4]. In this paper, we derive the right-hand sides and analyze the energy–momentum tensor in the framework of Vlasov–Maxwell–Einstein equations and Milne–McCrea models. New models of accelerated expansion of the Universe without Einstein's lambda are proposed.