**The model of the closed Universe ****with relativistic effects of extra dimension**

*Zahid Zakir* [1]

**Abstract**

In the standard general relativity (GR) a closed universe as a 3-sphere exists only at embedding into a real 4-space and a hypersurface of simultaneity of the universe is spherically-symmetric only in a global static frame where the center of the 3-sphere is rested. For this reason the evolution of the universe is described in a world time of this frame, where Einstein’s equations with homogeneous matter (without dark energy) have simple exact solutions. The radial speed of 3-sphere leads to the relativistic delay of proper times, which then leads to new expansion law and relativistic redshift. By using the initial data – present radius and velocity of expansion – other properties and evolution of the Universe are predicted and are in agreement with the data. As the result, from standard GR and observations follow that the Universe is closed, slowing down and the extra dimension probably really exist. The evolution is described for all epochs by taking into account pressure in earlier epochs. The nucleosynthesis and recombination occur at sufficiently smaller concentrations, but during sufficienly longer times. It is shown that the model is free on the cosmological problems of former approaches.

PACS: *04.20.Cv, 98.80.-k, 98.80.Jk **95.30.Sf, 97.60.Lf, 98.35.Jk, 98.54.-h, 98.80.-k, 04.60.-m *

*Key words: cosmological models, redshift, supernovae, Big Bang, nucleosynthesis, recombination, cosmic microwave background, cosmological problems** *

Vol. **8**, No 2, p. 37 – 61, v1, 15 May 2013

Online: TPAC: 4518-031 v1, 15 May 2013; DOI: 10.9751/TPAC.4518-031

[1] *Centre for Theoretical Physics and Astrophyics**, Tashkent, Uzbekistan*

zahidzakir@theor-phys.org

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