Problems of dark atom cosmology

The dark atoms $XHe$ are the composite Thomson like atomic dark matter candidates. We address two cosmological problems of this model. The excess of new superheavy particles with even negative charge $X^{-2n}$ over the corresponding antiparticles is balanced by sphaleron transitions with baryon asymmetry and the mass range of $X$ particles should be specified at which this excess can provide dominance of dark atoms in the dark matter density. The other problem is possible capture of light nuclei by dark atoms, which can lead to formation of anomalous isotopes. The possibility of formation of multi dark atom systems at the nucleosynthesis stage is also studied. We approach these open questions of dark atom cosmology in the present work.