Recently it was realized that the strong coupling scale in gravity substantially depends on the number of different quantum fields present in nature. On the other hand, gravity theory with an electroweak strong coupling scale could be responsible for a solution of the hierarchy problem. Consequently it was suggested that possible existence of very many hidden fields could stabilize the mass of Higgs particle. In this talk I review a cosmological scenario based on the assumption that the Standard Model possesses a large number of copies. It is demonstrated that baryons in the hidden copies of the standard model can naturally account for the dark matter. The right abundance of the hidden-sector baryons and the correct spectrum of density perturbations are simultaneously generated during modulated reheating. Surprisingly it turns out that for the natural values of inflaton coupling constants, the dark-matter abundance is predicted to be proportional to the ratio of observed cosmological parameters: the square of the amplitude of cosmological perturbations and the baryon-to-photon number ratio.