Baryon-dominated universe with macroscopically large antimatter regions

The whole set of astrophysical data indicates that our universe is globally baryon asymmetrical. Nevertheless a possibility of existence of relatively small amount of sufficiently large antimatter regions is not excluded. Such regions can survive the annihilation with surrounding matter only in the case if their sizes exceeds the certain scale. It is shown that the quantum fluctuations of a complex scalar field caused by inflation can lead to the origin of large antimatter domains progenitors, which contribute very insignificantly to the total volume of the universe. The resulting distribution and evolution of out-coming antimatter regions could cause every galaxy to be a harbor of an anti-star globular cluster. The existence of one of such anti-star globular cluster in our galaxy, would not disturb the observable γ-ray background, but the expected fluxes of anti-4He and anti-3He nuclei would be definitely accessible for the sensitivity of coming AMS02 experiment. (author)