Gravitational collapse, Friedman models and cosmological constant. Does the universe oscillate

The equivalency of the Tolman-Oppenheimer and Friedman methods is discussed. The solution of Oppenheimer and Snyder describes the Friedman flat Universe in a cosmological aspect. On the other hand, the Friedman results contain the description of gravitational collapse in the accompanying reference frame. It should be noted that the collapse and expansion of matter are phenomena connected indissolubly. The analysis of the cosmological consequences Λ ≠ 0 and the classification of homogeneous and isotropic Universe models is made. Using the obtained results, the hypothesis of a cyclic character of the Universe development is expressed. 7 refs.; 1 tab