Old and new puzzles of cosmology are reexamined from the point of view ofquantum theory of the universe developed here. It is shown that in proposedapproach the difficulties of the standard cosmology do not arise. The theorypredicts the observed dimensions of the nonhomogeneities of matter density andthe amplitude of the fluctuations of the cosmic background radiationtemperature in the Universe and points to a new quantum mechanism of theirorigin. It allows to obtain the value of the deceleration parameter which is ingood agreement with the recent SNe Ia measurements. The theory explains thelarge value of entropy of the Universe and describes other parameters.
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