Testing Bump in the Cosmological Power Spectrum Using Dwarf Galaxies

We analyze the possibility of using observational data on nearby dwarf galaxies -- their luminosity functions and spatial distributions -- to constrain deviations of the cosmological power spectrum from the standard one. Specifically, we consider a cosmological model with a "bump" in the power spectrum at a wavelength of 1.3~Mpc and a dimensionless amplitude $\mathcal{A}=2.0$. Such a spectrum is motivated by observations of an excess number of galaxies at high redshifts. The bump leads to a noticeable increase in the luminosity function in the range $-13 > M_B > -17$ at $z=0$. Comparison with observations constrains the bump amplitude to $\mathcal{A} < 0.25$ at a 3-sigma significance level for a wavelength of 1.3~Mpc. For wavelengths smaller than 0.8~Mpc, the bump manifests only in the luminosity function of dwarfs with $M_B > -14$.