We consider the impact of non-power-law spectra of matter perturbations with a bump or with a blue tilt at small scales on the evolution of supermassive black holes (SMBHs) located the innermost part of galaxies. We study SMBHs’ mass growth rate and the epochs of their birth in four cosmological models using N-body simulations of dark matter within the box of $(100\mathrm{Mpc}/h{)}^3$. The simulations were populated with SMBHs using the trinity semianalytic model. We found that the most massive SMBHs at the redshifts $z=5–6$ are similar in all considered cosmologies, including the standard lambda cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) model. At larger $z$ the bumpy spectra can provide a tenfold increase (relative to $\mathrm{\Lambda }\mathrm{CDM}$ model) in the masses of individual black holes without requiring super-Eddington accretion or heavy seeds. The nucleation of SMBHs starts at $z\sim 13$, which is earlier than in the standard $\mathrm{\Lambda }\mathrm{CDM}$ model.

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• Cosmology
• Dark matter
• Formation & evolution of stars & galaxies
• Astronomical black holes