%0 Journal Article %T A Study of Warm Dark Matter, the Missing Satellites Problem, and the UV Luminosity Cut-Off %A Bruce Hoeneisen %J International Journal of Astronomy and Astrophysics %P 25-38 %@ 2161-4725 %D 2023 %I Scientific Research Publishing %R 10.4236/ijaa.2023.131002 %X In the warm dark matter scenario, the Press-Schechter formalism is valid only for galaxy masses greater than the ¡°velocity dispersion cut-off¡±. In this work we extend the predictions to masses below the velocity dispersion cut-off, and thereby address the ¡°Missing Satellites Problem¡± of the cold dark matter ¦«CDM scenario, and the rest-frame ultra-violet luminosity cut-off required to not exceed the measured reionization optical depth. For warm dark matter we find agreement between predictions and observations of these two phenomena. As a by-product, we obtain the empirical Tully-Fisher relation from first principles. %K Cosmology: Dark Matter %K Galaxies: Statistics %U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=123819