Properties of Central Regions of the Dark Matter Halos in the Model with a Bump in the Power Spectrum of Density Perturbations

A surprisingly large number of galaxies with masses of $\sim10^9-10^{10}M_\odot$ at redshifts of $z\geq9$ are discovered with the James Webb Space Telescope. A possible explanation for the increase in the mass function can be the presence of a local maximum (bump) in the power spectrum of density perturbations on the corresponding scale. In this paper, it is shown that simultaneously with the growth of the mass function, galaxies from the bump region must have a higher density (compactness) compared to cosmological models without a bump. These more compact galaxies have been partially included in larger galaxies and have been subjected to tidal gravitational disruption. They have been less destructed than ``ordinary'' galaxies of the same mass, and some of them could survive to $z = 0$ and persist on the periphery of some galaxies. The formation and evolution of compact halos in a cube with a volume of $(47 \,\text{Mpc})^3$ with $(1024)^3$ dark matter particles in the redshift range from 120 to 0 have been numerically simulated and observational implications of the presence of such galaxies in the current Universe have been discussed.