On the Friedmann equation for the three-dimensional hypersphere

0462143 - MÚ 2017 RIV CZ eng C - Conference Paper (international conference)
Křížek, Michal - Mészáros, A.
On the Friedmann equation for the three-dimensional hypersphere.
Proceedings of the International Conference Cosmology on Small Scales 2016 : Local Hubble Expansion and Selected Controversies in Cosmology. Prague: Institute of Mathematics, Czech Academy of Sciences, 2016 - (Křížek, M.; Dumin, Y.), s. 159-178. ISBN 978-80-85823-66-0.
[Cosmology on Small Scales 2016. Prague (CZ), 21.09.2016-24.09.2016]
Institutional support: RVO:67985840
Keywords : Einstein's equations * standard cosmological model * dark matter * dark energy
Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics

The present standard cosmological model of the evolution of our universe, is based on the Friedmann equation, which was published by Alexander Friedmann in 1922. He applied Einstein’s equations to an expanding threedimensional sphere which enabled him to avoid boundary conditions. However, his description was very brief. Therefore, the main objective of this article is to detailed a derivation of the Friedmann equation for an unknown expansion function a = a(t) representing the radius of the universe. Furthermore, we present serious arguments showing why the validity of Einstein’s equations should not be extrapolated to the entire universe.
Permanent Link: http://hdl.handle.net/11104/0261654