Localized Enhancements of the Primordial Power Spectrum and the Abundance of Early Bright Galaxies

Abstract

Recent observations of bright galaxies at high redshifts by the James Webb Space Telescope have motivated renewed interest in cosmological mechanisms that can enhance the abundance of early massive dark matter halos. We study a phenomenological modification of the primordial curvature power spectrum in the form of a localized Gaussian enhancement. The modified spectrum is propagated to the linear matter power spectrum, the smoothed density variance, and the Sheth-Tormen halo mass function. We show that a bump centered at small scales can selectively enhance the abundance of rare high-redshift halos and, through a fixed semi-analytic mapping between halo mass and ultraviolet luminosity, shift the bright end of the UV luminosity function toward JWST measurements. The enhancement becomes more pronounced at higher redshift due to the exponential sensitivity of the rare-halo tail to the variance. We emphasize that the effect is limited by small-scale power-spectrum constraints, particularly Lyman-$α$ forest data, and should be interpreted as a partial cosmological contribution rather than a complete solution to the JWST galaxy tension.