On a Probable Contribution of the Einstein-Podolsky-Rosen Effect to   Solving the Problem of Homogeneity of the Universe
  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. 
Yu.V. Dumin