Universal Acceleration and Fuzzy Dark Matter

Observations of velocity dispersions of galactic structures over a wide range of scales point to the existence of a universal acceleration scale $a_0\sim {10}^{-10}$ m/s${}^2$. Focusing on the fuzzy dark matter paradigm, which proposes ultralight dark matter with mass around ${10}^{-22}$ eV and de Broglie wavelength $\lambda \sim \mathrm{f}\mathrm{e}\mathrm{w}\times {10}^2$ parsecs, we highlight the emergence of the observed acceleration scale from quantum effects in a fluid-like description of the dark matter dynamics. We then suggest the possibility of a natural connection between the acceleration scale and dark energy within the same paradigm.