  Search for the mechanisms suppressing formation of Higgs field defects (e.g.
domain walls) during the cosmological phase transitions is one of key problems
in explanation of the observed large-scale uniformity of the space-time. One of
the possible solutions can be based on accounting for Einstein-Podolsky-Rosen
(EPR) correlations. Namely, if a coherent quantum state of the Higgs field was
formed in the course of its previous evolution, then reduction to the state
with broken symmetry during the phase transition should be correlated even at
the scales exceeding the local cosmological horizons. Detailed consideration of
the simplest one-dimensional cosmological model with Z2 Higgs field
demonstrates that, at certain parameters of the Lagrangian, EPR-correlations
really result in a substantial suppression of spontaneous formation of the
domain walls.
