Isotropic Space with Discrete Gravitational-Field Sources. On the Theory of a Nonhomogeneous Isotropic Universe

Existing cosmological theories are based on Einstein's law of gravitation (7). In this equation the average is taken only in the right-hand side by a substitution of the energy momentum tensor corresponding to uniform and continuous distribution of matter. In this paper a new cosmological equation (48), which is more correct from the physical and mathematical point of view, is obtained by space-time averaging of all the terms of Eq. (7) and taking into account the fluctuations of the gravitational field due to nonuniformities in the distribution of matter. An estimate of these fluctuations within the framework of Newton's approximation leads to the cosmological equations (51), (52) and (53) for flat space and positive and negative curvature. The solutions of these equations, in distinction from all the variants of Friedman's theory, do not have a singular point for some initial moment of time with an infinitely large density of matter. However, this result follows when the relations obtained are extrapolated beyond the range of their applicability, and therefore final conclusions can be made on the basis of the solutions of the new cosmological equations (48) when we go beyond the Newtonian approximation.