Spontaneous symmetry breaking in a closed cosmological Friedmann model

Spontaneous symmetry breaking in a closed Friedmann model is investigated. Conditions of symmetry breaking for a space with finite volume are derived. It is shown in the single-loop approximation that in the model of a self-interacting scalar field and in scalar electrodynamics the symmetry is restored at small radii of the Universe irrespective of the sign of the square of the mass, and for scalar electrodynamics irrespective of the relationship between the coupling constants as well. The obtained results make it possible to analyze numerous cosmological consequences of vacuum phase transitions in the early Universe. The Appendix describes the general solution of the equations of a massive vector field in a closed static Friedmann model.