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
$z\approx 6$ in the Hubble Frontier Fields (HFF) provides stringent constraints
on the parameter space of i) Dark Matter models based on keV sterile neutrinos;
ii) the "fuzzy" wavelike Dark Matter models, based on Bose-Einstein condensate
of ultra-light particles. For the case of the sterile neutrinos, we consider
two production mechanisms: resonant production through the mixing with active
neutrinos and the decay of scalar particles. For the former model, we derive
constraints for the combination of sterile neutrino mass $m_{\nu}$ 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 the scalar to the 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 $\approx 1/{\rm Mpc}^3$ of high-redshift galaxies in the HFF
sets a lower limit $m_\psi\geq 8\cdot 10^{-22}$ eV (at 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 redshifts.
