A mathematical theory of the accelerated expansion of the Universe based on the principle of least action

V. V. Vedenyapin, Ya. G. Batishcheva, M. V. Goryunova, A. A. Russkov

Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, Moscow, Russia

Abstract: In classical works, the equations for gravitational and electromagnetism fields are proposed without deriving the right-hand sides. Here, we derive the right-hand sides and analyze the energy–momentum tensor within the framework of the Vlasov–Maxwell–Einstein equations and consider cosmological models such as Milne–McCrea and Friedmann. This allows us to place General Relativity (GR) on a rigorous mathematical foundation: to derive a closed system of GR equations from the principle of least action and provide a rigorous definition of cosmological solutions. This explains the accelerated expansion of the Universe without Einstein's lambda, dark energy, or fantastic new fields, but as a simple relativistic effect.

Keywords: general theory of relativity, Vlasov equation, Vlasov–Einstein equation, Vlasov–Maxwell equation, Vlasov–Poisson equation, accelerated expansion of the Universe, Hubble constant.

UDC: 517.958

DOI: 10.22363/2413-3639-2025-71-4-562-584