Antimatter regions in the baryon-dominated Universe

Quantum fluctuations of a complex, baryonic charged scalar field caused by inflation can generate large domains, which convert later into antimatter regions. As a result the Universe can become globally matter-dominated, with minor contribution of antimatter regions. The distribution and evolution of such antimatter regions could cause every galaxy to be a harbour of an anti-star globular cluster. At the same time, the scenario does not lead to large-scale isocuvature perturbations, which would disturb observable CMB anisotropy. The existence of one of such antistar globular cluster in our Galaxy does not contradict the observed $\gamma$-ray background, but the expected fluxes of $\bar{\rm ^4He}$ and $\bar{\rm ^3He}$ from such an antimatter object are definitely accessible to the sensitivity of the coming AMS--02 experiment.