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The statement and solution of the problem of the expansion of the Universe in nonstationary spherically-symmetric coordinates in the Schwarzschild metric are considered without pressure taken into account. The observational data of astronomers investigating the rates of recession of distant stars are explained on the basis of the obtained solutions. [ABSTRACT FROM AUTHOR]

On the basis of the special relativity theory (SRT), the mean density of matter in the Universe is calculated with the relativistic kinetic energy of receding galaxies taken into account. Within the framework of the general relativity theory (GRT), we estimate the influence on the mean density of the effect of gravitation. A contradiction between the hypothesis of dark energy and conclusions following from SRT and GRT is noted. [ABSTRACT FROM AUTHOR]