Ultralight scalars as cosmological dark matter Lam Hui, Jeremiah P. Ostriker, Scott Tremaine, and Edward Witten propose that dark matter could be composed of ultralight bosons, known as fuzzy dark matter (FDM), with masses around $10^{-22}$ eV. This hypothesis is motivated by the need to explain discrepancies in the predictions of the standard cold dark matter (CDM) model on galactic scales. FDM particles have a large de Broglie wavelength, which suppresses small-scale structure formation and leads to the formation of soliton cores in dark matter halos. These cores are stable, minimum-energy solutions of the Schrödinger-Poisson equation and are surrounded by envelopes resembling CDM halos. The transition between soliton and envelope is governed by relaxation processes similar to two-body relaxation in gravitating systems. FDM can influence the structure of galaxies, including the stellar disk and bulge, but has minimal effects on disk thickening or globular cluster disruption. FDM halos can evaporate through tunneling, limiting the minimum sub-halo mass within the Milky Way. The FDM hypothesis is consistent with current observations of high-redshift galaxies and late reionization, but faces tension with observations of the Lyman-α forest. FDM could also affect the formation of supermassive black holes and their mergers. The paper discusses the astrophysical consequences of FDM, including its potential to explain the cusp-core problem in dwarf spheroidal galaxies. The authors conclude that FDM is a viable alternative to CDM, with observational tests needed to confirm its validity.Ultralight scalars as cosmological dark matter Lam Hui, Jeremiah P. Ostriker, Scott Tremaine, and Edward Witten propose that dark matter could be composed of ultralight bosons, known as fuzzy dark matter (FDM), with masses around $10^{-22}$ eV. This hypothesis is motivated by the need to explain discrepancies in the predictions of the standard cold dark matter (CDM) model on galactic scales. FDM particles have a large de Broglie wavelength, which suppresses small-scale structure formation and leads to the formation of soliton cores in dark matter halos. These cores are stable, minimum-energy solutions of the Schrödinger-Poisson equation and are surrounded by envelopes resembling CDM halos. The transition between soliton and envelope is governed by relaxation processes similar to two-body relaxation in gravitating systems. FDM can influence the structure of galaxies, including the stellar disk and bulge, but has minimal effects on disk thickening or globular cluster disruption. FDM halos can evaporate through tunneling, limiting the minimum sub-halo mass within the Milky Way. The FDM hypothesis is consistent with current observations of high-redshift galaxies and late reionization, but faces tension with observations of the Lyman-α forest. FDM could also affect the formation of supermassive black holes and their mergers. The paper discusses the astrophysical consequences of FDM, including its potential to explain the cusp-core problem in dwarf spheroidal galaxies. The authors conclude that FDM is a viable alternative to CDM, with observational tests needed to confirm its validity.