Polarization of photons emitted in weak decays occuring at distant star allows to determine whether this star is made from antimatter. Even more promissing is the observation of neutrinos (antineutrinos) produced at neutronization (antineutronization) reactions at the beginning of SN (SN ) explosion.According to the Standard Cosmological Model (SCM) no primordial antimatter remains in the Universe. Let us shortly remind the arguments which lead to this conclusion. When in the course of the post Big Bang expansion the universe cooled down below the QCD phase transition at T QCD = 100 − 200 MeV, baryon-antibaryon pairs started to annihilate. If the baryon number of the Universe at these temperatures was locally zero, then the remaining frozen concentration of baryons would be (see e.g. ref.[1]):where n B is the number density of baryons, by assumption equal to that of antibaryons, and n γ is the number density of photons in CMB. This result is by factor 10 11 smaller than the presently observed baryon concentration, which can be e.g. deduced from the recent Planck data [2], as:with the precision at the per cent level. Here it is implicitly assumed that the amount of antibaryons is negligibly small, nB ≪ n B . In order to avoid conclusion (1) we have either to assume that at the era of baryon-antibaryon annihilation the universe was predominantly and homogeneously populated by baryons, or that the universe has domain structure with spatially separated domains of matter and antimatter. In the last case it might be even not excluded that the total baryonic number of the universe is zero.In the frameworks of the SCM the first option is accepted, which has a strong support from the baryogenesis theory, whose basic principles have been formulated by Sakharov almost half a century ago [3]. In all known scenarios of baryogenesis an excess of baryons over antibaryons was generated at very (or rather) high temperatures, while at the subsequent cosmological expansion and cooling down the baryon-to-photon ratio (2) stayed approximately constant, up to the entropy release by the massive particle annihilation.In the universe with an excess of baryons a chance for antibaryons to survive was negligibly small, though in the early universe there were almost equal number densities of baryons and antibaryons, (n B − nB)/n B ≈ η ≪ 1 . The temperature at which the "massacre" of antibaryons by dominant baryons stopped is fixed by the annihilation freezing which is determined by the time when the annihilation rate became equal to the cosmological expansion rate:where σv ≈ 1/m 2 π is the cross-section of pp → nπ reaction times the proton velocity in c.m. system, m p is the proton mass, M p is the Planck mass and n is the number of pions produced in pp annihilation.That is why the remaining antiproton concentration being proportional tois unobservably small: there is not a single primordial antiproton in all presently visible part of our Universe. This bound is evidently too strong. Statistical fluctuations of the antibaryonic density coul...