  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.
