  Evading formation of the domain walls in cosmological phase transitions is
one of key problems to be solved for explanation of the observed large-scale
homogeneity of the Universe. The previous attempts to get around this obstacle
led to imposing severe observational constraints on the parameters of the
fields involved. Aim of the present report is to show that yet another way to
overcome the above problem is accounting for Einstein-Podolsky-Rosen (EPR)
effect. Namely, if the scalar (Higgs) field was presented by a single coherent
quantum state at the initial instant of time, then its reduction during a phase
transition at some later instant should be correlated even at distances
exceeding the local cosmological horizon. Consideration of a simplest
one-dimensional cosmological model with Z_2 Higgs field demonstrates that EPR
correlations can substantially reduce the probability of spontaneous creation
of the domain walls, and such effect seems to be even more promising in the
cases of two- and three-dimensional geometry.
