Fundamental Physics with the Hubble Frontier Fields: Constraining Dark Matter Models with the Abundance of Extremely Faint and Distant Galaxies

We show that the measured abundance of ultra-faint lensed galaxies at z approximate to 6 in the Hubble Frontier Fields (HFF) provides stringent constraints on the parameter space of (i) dark matter models based on. keV sterile neutrinos; (ii) fuzzy wavelike dark matter models, based on Bose-Einstein condensates of ultra-light particles. For the case of sterile neutrinos, we consider two production mechanisms: resonant production through mixing with active neutrinos and the decay of scalar particles. For the former model, we derive constraints for the combination of sterile neutrino mass m(v) and mixing parameter sin(2)(2 theta) which provide the tightest lower bounds on the mixing angle (and hence on the lepton asymmetry) derived so far by methods independent of baryonic physics. For the latter we compute the allowed combinations of the scalar mass, its coupling to the Higgs field, and the Yukawa coupling of scalar to sterile neutrinos. We compare our results to independent existing astrophysical bounds on sterile neutrinos in the same mass range. For the case of fuzzy dark matter, we show that the observed number density approximate to 1/Mpc(3) of high-redshift galaxies in the HFF sets a lower limit . m(psi) >= 8 center dot 10(-22) eV (at the 3-sigma confidence level) on the particle mass, a result that strongly disfavors wavelike bosonic dark matter as a viable model for structure formation. We discuss the impact on our results of uncertainties due to systematics in the selection of highly magnified, faint galaxies at high redshift.