Excess of high-z galaxies as a test for bumpy power spectrum of density perturbations

ABSTRACT 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 k0 and run N-body simulations in a cube (5 Mpc h−1)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 cold dark matter (ΛCDM), 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 ΛCDM, therefore the models with the bumpy spectra can be identified in observations by their excess in number of bright sources at high redshift only.