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Starting from the relativistic dynamics of homogeneous expanding ball, a relativistic evolution equation for the closed model of the Universe is formulated which correctly takes into account a relativistic time dilation of proper times due to different expansion speeds at different epochs. The hypersurface of simultaneity of the Universe is spherically-symmetric only in the rest frame of 3sphere’s centre and, consequently, the evolution is described in world time t of this frame of reference. This relativistic evolution equation coincided with Einstein's equation for a 3-sphere expanding in 4space (without dark energy) and has a simple exact solution. There is a relativistic redshift leading to new relation of redshift with the scale factor which then gives new “luminosity-redshift” relation well describing the data for Type 1а supernovae at admissible parameters. By using the initial data – present radius and expansion speed other properties and evolution of the Universe are predicted. The model predicts that the observing baryon density is one third of total matter density and remaining two third is dark matter density. The accounting of stasis effects slightly changes the parameters only. 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

The closed model of the universe with relativistic redshift