100 years of the Friedmann equation

0559513 - MÚ 2023 RIV CZ eng C - Konferenční příspěvek (zahraniční konf.)
Křížek, Michal
100 years of the Friedmann equation.
Proceedings of the International Conference Cosmology on Small Scales 2022 : Dark Energy and the Local Hubble Expansion Problem. Prague: Institute of Mathematics CAS, 2022 - (Křížek, M.; Dumin, Y.), s. 131-144. ISBN 978-80-85823-72-1.
[Cosmology on Small Scales 2022. Prague (CZ), 21.09.2022-24.09.2022]
Institucionální podpora: RVO:67985840
Klíčová slova: Einstein's equations * modeling error * incorrect extrapolations * dark matter
Obor OECD: Astronomy (including astrophysics,space science)
https://css2022.math.cas.cz/proceedingsCSS2022.pdf

In 1922, Alexander Friedmann applied Einstein’s equations to a three-dimensional sphere to describe the evolution of our universe. In this way he obtained a nonlinear ordinary differential equation (called after him) for the expansion function representing the radius of that sphere. At present, the standard cosmological ΛCDM model of the universe is based just on the Friedmann equation. It needs a significant amount of dark matter, about six times that of the usual baryonic matter, besides an even larger amount of dark energy to be consistent with the real universe. But to date, both dark matter and dark energy have remained without concrete evidence based on direct physical measurements. We present several arguments showing that such a claimed amount of dark matter and dark energy can only be the result of vast overestimation, incorrect extrapolations, and that it does not correspond to the real universe. The spatial part of our universe seems to be locally flat and thus it can be locally modeled by the Euclidean space. However, Friedmann did not consider the flat space with zero curvature. Therefore, in the second part of this paper we will derive a general form of the corresponding metric tensor satisfying Einstein’s equations with zero right-hand side.
Trvalý link: https://hdl.handle.net/11104/0332789