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.