Barabash O. Quasiclosed worlds and field-theoretic methods in cosmology.

In the first section of the thesis, we consider the question about Newtonian limit in conformal gravity. We find a solution of the equations of the conformal gravity in vacuum in the Newtonian approximation for the case of spherically symmetrical and static field in gauge, when mass of elementary particles are constant. In the second section of the thesis, we study the dynamics of cosmic texture in a Friedman universe. For solving this problem, an approximate method is applied for the first time, which makes it possible to find the conditions of collapse of textures depending on the law of expansion of the universe and its topology. In the third section of the thesis, we propose an approximate approach to the description of the microstructure of space-time in terms of quasiclosed worlds (QCW). We obtained the equation that governs the wave function of a QCW in the minisuperspase approximation and find the probability of tunneling through the barrier.