The modern Standard cosmological scenario, reflecting to large extent the development of A.D.Sakharov’s legacy in cosmoparticle physics, involves inflation, baryosynthesis and dark matter/energy. Physics of all these elements of the cosmological paradigm lays Beyond the Standard model (BSM) of elementary particles and involves in its turn cosmological probes for its study. To specify this physics the idea of multi-messenger probes of new physics is proposed, involving the set of additional model dependent consequences of physical models for inflation, baryosynthesis and dark matter. After brief review of Cosmophenomenology of new physics, we concentrate on probes for mechanisms of baryosynthesis, first proposed by A.D.Sakharov, which are of special interest in this context. Antimatter domains formed in the early Universe can reflect possible strong nonhomogeneity of baryosyntehsis. In homogeneous and isotropic Universe such nonhomgeneity is determined by specific model dependent choice of mechanisms of inflation and baryosynthesis. These mechanisms are beyond the standard model of elementary particles and provide tests for the physics, underlying the modern cosmology. Constraints on macroscopic antimatter objects or cosmic fuxes of antinuclei provide probes for the corresponding models. Positive evidence for maroscopic antimatter existence leads beyond the standard paradigm of the cosmological scenario and specify with high precision the parameters of BSM physics .