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 ΛCDM 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.
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