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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., Comment: 8 pages, 6 figures

We consider three cosmological models with non-power-law spectra of primordial density perturbations and test them against $\Lambda$CDM in density profiles. We found that, despite the significant difference in initial conditions, the mean density profiles of all models are still close to the Navarro-Frenk-White one, albeit with some dispersion. We demonstrate that the density profile slopes in the innermost part of halo have a significant evolution with $z$, which can be used to identify the cosmological model. We also present a toy model resulting in the appearance of core in the central part of gravitationally bound dark matter halo., Comment: 9 pages, 6 figures, submitted to Phys. Rev. D

The initial power spectrum of density perturbations, generated during the inflationary epoch, is now constrained by observations on scales $\lambda>5$~Mpc and has a power-law form. The peculiarities of the inflationary process can lead to the appearance of non-power-law contributions to this spectrum, such as peaks. The exact size and shape of the peak cannot be predicted in advance. In this paper, we propose methods for searching for such peaks in the region of the spectrum with $\lambda<5$~Mpc. Perturbations on these scales enter the nonlinear stage at $z\gtrsim10$, which is now becoming accessible to observations. Our studies of numerical models of large-scale structure with peaks in the initial spectrum have shown that spectral features on scales with $\lambda>0.1$~Mpc manifest in the clustering of galaxies, as well as affect their mass function, sizes, and density. Studying these characteristics of distant galaxies will allow us to constrain cosmological models with peaks., Comment: 11 pages, 5 figures, accepted in Astrophysical Bulletin

Modified matter power spectra with approximately Gaussian bump on sub-Mpc scales can be a result of a complex inflation. We consider five spectra with different Gaussian amplitudes $A$ and locations $k_0$ and run N-body simulations in a cube $(5 Mpc/h)^3$ at $z>8$ to reveal the halo mass functions and their evolution with redshift. We have found that the Sheth-Tormen formula provides a good approximation to a such kind of halo mass functions. In the considered models the dark matter halo formation starts much more earlier than in $\Lambda$CDM, which in turn can result in an earlier star formation and a nuclear activity in galaxies and can be detected and tested by, e.g., JWST. At $z=0$ the halo mass functions are hardly distinguishable from the standard $\Lambda$CDM, therefore the models with the bumpy spectra can be identified in observations by their excess in number of bright sources at high redshift only., Comment: 9 pages, 5 figures, submitted to MNRAS

The extragalactic background radiation produced by distant galaxies emitting in the far infrared limits the sensitivity of telescopes operating in this range due to confusion. We have constructed a model of the infrared background based on numerical simulations of the large-scale structure of the Universe and the evolution of dark matter halos. The predictions of this model agree well with the existing data on source counts. We have constructed maps of a sky field with an area of 1 deg$^2$ directly from our simulated observations and measured the confusion limit. At wavelengths $100-300$ $\mu$m the confusion limit for a 10-m telescope has been shown to be at least an order of magnitude lower than that for a 3.5-m one. A spectral analysis of the simulated infrared background maps clearly reveals the large-scale structure of the Universe. The two-dimensional power spectrum of these maps has turned out to be close to that measured by space observatories in the infrared. However, the fluctuations in the number of intensity peaks observed in the simulated field show no clear correlation with superclusters of galaxies; the large-scale structure has virtually no effect on the confusion limit., Comment: 10 pages, 4 figures