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Cosmology on Small Scales 2022: Dark Energy and the Local Hubble Expansion Problem
Křížek, Michal ; Dumin, Y. V.
One hundred years ago, Russian mathematician and physicist Alexander A. Friedmann applied the system of Einstein equations to the three-dimensional sphere with a time varying radius. In this way, he obtained a nonlinear ordinary differential equation which is called the Friedmann equation after him and serves now as a cornerstone of the standard cosmological model. Unfortunately, it is well known that this model exhibits a number of paradoxes. Thus, the main goal of the CSS 2022 Conference Proceedings is to discuss whether and how the Friedmann equation can be applied at the various spatial scales, from our local cosmic neighborhood up to the whole Universe, and if the existence of dark matter and dark energy are merely artifacts of the excessive extrapolations.
100 years of the Friedmann equation
Křížek, Michal
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.

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