This work is based on modification of the general relativity, which includes effects of production /absorption of matter by the vacuum. The theory (without fitting parameters) is in good quantitative agreement with cosmological observations (SnIa, SDSS-BAO and reduction of acceleration of the expanding universe). In this theory, there is no Big Bang at the beginning, but some local bangs during the evolution are probable. Also, there is no critical density of the universe and, therefore, no dark energy. Based on exact Gaussian solution for the scale factor, it is shown that an effective age of the universe is about 327 billion years. Production of primary dark matter particles have started 43 billion years later. It is shown that characteristic distance between particles is 30 times smaller than the thermal de Brogle wavelength, so that quantum effects, including formation of the Bose-Einstein condensate, can dominate. "Ordinary" matter was synthesized from dark matter in galaxies. Supplementary exact solutions are obtained for various ranges of parameters. From the theory we get an interface between dark and ordinary matter (IDOM), which very likely exist not only in cosmos, but everywhere, including our body and our brain. Key words: cosmology; age of the universe; dark matter; interface between dark and ordinary matter.