On Mechanics of the Universe Evolution

The paper is devoted to the problem of cosmology, which is formulated as a spherically symmetric problem for a pressure-free model of continuum. The problem is described by equations of general relativity corresponding to the special four-dimensional space, which is Euclidean with respect to space coordinates and Riemannian with respect to the time coordinate only. Within the framework of this model, the analytical solution of the field equations incorporating the cosmological constant is obtained and analyzed. This solution describes the continuous process of the Universe evolution, consisting of the phases—the Universe expansion and subsequent gravitational collapse. The existing data for the observable Universe age and the cosmological constant are used for numerical evaluations. As a result, the obtained solution specifies the dependency of the continuum density on time and allows us to evaluate the durations of the processes of the Universe expansion and gravitational collapse.