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Explore the theoretical framework and observational implications of ultralight dark matter in this comprehensive lecture that examines how these exotic particles with masses many orders of magnitude smaller than conventional dark matter candidates could reshape our understanding of cosmic structure formation. Delve into the unique properties of ultralight dark matter, including its wave-like behavior on galactic scales and its potential to resolve small-scale discrepancies in the standard cold dark matter paradigm. Learn about the mathematical formalism describing ultralight dark matter dynamics, including the Schrödinger-Poisson equations and their solutions in various cosmological contexts. Investigate observational signatures and constraints from galaxy formation, the cosmic microwave background, and large-scale structure surveys that can distinguish ultralight dark matter from conventional models. Examine current theoretical challenges and future prospects for detecting or ruling out ultralight dark matter scenarios through upcoming astronomical observations and improved numerical simulations.
