  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
$\lambda\sim {\rm few}\times10^{2}$ 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.
