Spontaneous symmetry breaking in an open Friedmann universe

Problem of spontaneous symmetry breaking is studied in the model of self-interacting scalar field with minimal interaction with gravitational field in the external static Friedmann's metric of the open type. It is shown that the symmetry breaking does not occur in the model with the positive square of the mass. In the model with the negative square of the mass the symmetry is restored at early stages of the evolution of the Universe. In the massless model there is the symmetry breaking at sufficiently large scale factors, however when the scale factors are exponentially large, one must go beyond the perturbation theory framework to study the behaviour of the symmetry.