  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 exceed a certain scale. It is shown that quantum fluctuations of
a complex scalar field caused by inflation can generate large antimatter
domains progenitors, which contribute insignificantly to the total volume of
the Universe. The resulting distribution and evolution of such antimatter
regions could cause every galaxy to be a harbour of an anti--star globular
cluster. The existence of one of such anti -- star globular cluster in our
Galaxy, does not contradict the observed $\gamma$ -- ray background, but the
expected fluxes of $\bar{^4He}$ and $\bar{^3He}$ from such an antimatter object
can be searched for in PAMELA experiment and are definitely accessible for the
sensitivity of coming AMS02 experiment.
