BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:V.V. Vedenyapin (Keldysh Institute of Applied Mathematics\, Russia n Academy of Sciences\, Moscow) DTSTART:20260423T110000Z DTEND:20260423T120000Z DTSTAMP:20260423T022229Z UID:mmandim/111 DESCRIPTION:Title: Cosmological solutions\, Hubble's law\, and accelerated expansion of the universe from the principle of least action\nby V.V. Vedenyapin (Keld ysh Institute of Applied Mathematics\, Russian Academy of Sciences\, Mosco w) as part of Mathematical models and integration methods\n\n\nAbstract\nI n classic textbooks [1-3]\, the Hubble constant is defined in terms of the metric. Here\, we define it\, as expected\, in terms of matter\, followin g Milne and McCrea\, extending their theory of an expanding universe to th e relativistic case. This allows us to explain the accelerated expansion a s a simple relativistic effect\, without Einstein's lambda\, dark energy\, or new particles\, as an exact consequence of Einstein's classical action . The well-verified fact of accelerated expansion allows us to determine t he sign of the curvature in the Friedmann model: it turns out to be negati ve\, and we live in Lobachevsky space. Also in classical works (see [1–4 ])\, equations for the fields are proposed without deriving the right-hand sides. Here we give a derivation of the right-hand sides of the Maxwell a nd Einstein equations within the framework of the Vlasov–Maxwell–Einst ein equations from the classical\, but slightly more general principle of least action [5–6]. The resulting derivation of Vlasov-type equations yi elds Vlasov–Einstein equations that differ from those proposed previousl y. A method for transition from kinetic equations to hydrodynamic conseque nces is proposed [5–6]\, as was previously done by A.A. Vlasov himself [ 4]: this can be interpreted as a transition from a kinetic turbulent descr iption using a distribution function to a laminar description of the hydro dynamic type. This yields cosmological solutions of the Milne–McCrea typ e. In the case of Hamiltonian mechanics\, a transition from the hydrodynam ic consequences of the Liouville equation to the Hamilton-Jacobi equation is possible\, as was already done in quantum mechanics by E. Madelung\, an d more generally by V.V. Kozlov [7] and V.P. Maslov. This yields Milne–M cCrea solutions in the nonrelativistic case\, as well as nonrelativistic a nd relativistic analyses of Friedmann-type solutions to the nonstationary evolution of the Universe. This allows us to obtain the fact of the accele rated expansion of the Universe as a relativistic effect [8-10] without ar tificial additions such as Einstein's lambda\, dark energy\, and new field s\, from the classical relativistic principle of least action. This places general relativity and cosmology on a solid mathematical foundation and m akes it possible to explain the accelerated expansion\, a well-tested expe riment (with a Nobel Prize in 2011).\n\nReferences.\n\n1. Dubrovin\, B. A. \, Novikov\, S. P.\, and Fomenko\, A. T. “Modern Geometry: Methods and A pplications.” Moscow: Nauka\, 1986.\n\n2. Landau\, L. D.\, Lifshitz\, E. M. “Field Theory.” Moscow: Nauka\, 1988.\n\n3. Weinberg\, S. “Gravi tation and Cosmology.” Moscow: Mir\, 1975\, 696 p.\n\n4. Vlasov\, A. A. “Statistical Distribution Functions.” Moscow: Nauka\, 1966\, 356 p.\n\ n5. Vedenyapin\, V.\, Fimin\, N.\, Chechetkin\, V. “The generalized Frie dmann model as a self-similar solution of the Vlasov–Poisson equation sy stem.” European Physical Journal Plus. 2021. Vol. 136. No. 1. P. 71.\n\n 6. V. V. Vedenyapin\, V. I. Parenkina\, S. R. Svirshchevskii\, “Derivati on of the Equations of Electrodynamics and Gravity from the Principle of L east Action”\, Comput. Math. Math. Phys.\, 62:6 (2022)\, 983–995.\n\n7 . Kozlov V. V.\, General Theory of Vortices\, Udmurt University Press\, Iz hevsk\, 1998\, 239 p.\n\n8. V. V. Vedenyapin\, “Mathematical theory of t he expanding Universe based on the principle of least action”\, Russ. Co mput. Math. and Math. Phys.\, 64:11 (2024)\, 2114–2131\n\n9. V. V. Veden yapin\, Ya. G. Batishcheva\, M. V. Goryunova\, and A. A. Russkov\, “Math ematical theory of the accelerating expansion of the Universe based on the principle of least action”\, CMFD\, 71:4 (2025)\, 562–584.\n LOCATION:https://researchseminars.org/talk/mmandim/111/ END:VEVENT END:VCALENDAR