  We study the impact of gravitational slingshot on the distribution of cold
dark matter in early and modern era galaxies. Multiple gravitational encounters
of a lower mass dark matter particle with massive baryonic astrophysical bodies
would lead to an average energy gain for the dark matter, similar to second
order Fermi acceleration. We calculate the average energy gain and model the
integrated effect on the dark matter profile. We find that such slingshot
effect was most effective in the early history of galaxies where first
generation stars were massive, which smeared the dark matter distribution at
the galactic center and flattened it from an initial cusp profile. On the other
hand, slingshot is less effective after the high mass first generation stars
and stellar remnants are no longer present. Our finding may help to resolve the
cusp-core problem, and we discuss implications for the existing
observation-simulation discrepancies and phenomena related to galaxy mergers.
