  Evading formation of the domain walls in cosmological phase transitions is
one of the key problems to be solved for getting agreement with 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. Our aim is to show that yet another way to
overcome the above problem is accounting for EPR effect. Namely, if the scalar
(Higgs) field was presented by a single 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. By
considering a simplest 1D model with Z_2 Higgs field, we demonstrate that EPR
effect really can substantially reduce the probability of spontaneous creation
of the domain walls.
