Fuzzy Dark Matter: The de Broglie Scale of an Ultralight Axion Against Lyman-Alpha Forest Bounds

At 10^-22 eV the wavelength is 0.60 kpc, the scale that made the idea attractive for dwarf-galaxy cores. At the forest bound of 2 x 10^-21 eV it shrinks to 0.030 kpc, smaller by a factor of 20.0, and at 10^-23 eV it would extend to 6.0 kpc. The bound density of 9.72e+54 g per cubic centimetre does not enter the wavelength formula at any point; the tension between the classic mass and the forest bound is a late-universe, structure-formation tension. The de Broglie wavelength falls from 0.60 kpc at the classic mass to 0.030 kpc at the Lyman-alpha bound, a factor of 20.0, and this tension is independent of the bounce. This study is computed from stated assumptions and published comparison values; it is not a measurement.