Reliable Tests of Faint-end UV Luminosity Functions in Strong Lensing Fields

Dark matter comprises ~85% of the entire mass of the Universe, but the fundamental nature of its constituent particles remains elusive. In this thesis, I test for two competitive dark matter models: the conventional heavy particle paradigm, and dark matter being ultralight bosons of mass $\sim 10^{-22}$eV ($\psi$DM). More specifically, I test for the faint-end turnover induced by $\psi$DM models, exploiting the strong lensing power by massive galaxy clusters to probe intrinsically fainter magnitudes. A key challenge for such an analysis would be contamination by low-z galaxies sharing similar observed SEDs as high-z galaxies. As I will demonstrate, such a contamination issue is generally severe and may wash out the faint-end turnover signatures. I also show that $\sim 50\%$ of the purported $3.5\leq z\leq 5.5$ galaxies within existing photometric redshift catalogs constructed for Hubble Frontier Fields (HFF) are in fact low-z interlopers. Luckily, individual mitigation of interlopers can be achieved with the combination of deep HST and JWST observations. For fields without supplementary data, machine learning methods will be shown useful in preserving the mitigating power. Cleaner $3.5\leq z\leq 5.5$ and $6\leq z\leq 10$ samples are derived for a more reliable test in strong lensing field of MACS J0416, with which I found no evidence for faint-end turnovers, leading to a constraint on the $\psi$DM mass of $>2.97\times10^{-22}$eV at 95\% confidence. This constraint will also be interpreted in an scheme where dark matter is composed of multiple particle copies, where I argue the derived mass bound is likely on an effective de Broglie scale governing the collective behavior of the entire $\psi$DM budget under gravitational equilibrium established.