After a brief overview of methods of cosmoparticle physics, studying fundamental relationship of cosmology and particle phsyics in combination of physical, astrophysical and cosmological probes minimal extensions of the Standard model, predicting existence of stable double charged particles is considered. The possibility of dark atoms, in which stable -2 charged particles are bound with primordial helium nucleus, can explain the puzzles of direct dark matter search. Physical, astrophysical and cosmological probes for this hypothesis are discussed.