What is the Halo Mass Function in a Fuzzy Dark Matter Cosmology?
  Fuzzy dark matter (FDM) or wave dark matter is an alternative theory designed
to solve the small-scale problems faced by the standard cold dark matter
proposal for the primary material component of the universe. It is made up of
ultra-light axions having mass $\sim 10^{-22}$ eV that typically have de
Broglie wavelength of several kpc, alleviating some of the apparent small-scale
discrepancies faced by the standard $\Lambda$CDM paradigm. In this paper, we
calculate the halo mass function for the fuzzy dark matter using a sharp-k
window function and compare it with one calculated using numerical simulations,
finding the peak mass at roughly $10^{10} {M_{\odot}}$ for a particle mass of
$2\times 10^{-22}$ eV. We also constrain the mass of FDM particle to be
$\gtrapprox 2\times10^{-22}$ eV using the observations of high-redshift ($z\sim
10$) lensed galaxies from CLASH survey.
