Constraints on axionic fuzzy dark matter from light bending and Shapiro
  time delay
  Ultralight axion like particles (ALPs) of mass $m_a\in
(10^{-21}\rm{eV}-10^{-22}\rm{eV})$ with axion decay constant $f_a\sim
10^{17}\rm{GeV}$ can be candidates for fuzzy dark matter (FDM). If celestial
bodies like Earth and Sun are immersed in a low mass axionic FDM potential and
if the ALPs have coupling with nucleons then the coherent oscillation of the
axionic field results a long range axion hair outside of the celestial bodies.
The range of the axion mediated Yukawa type fifth force is determined by the
distance between the Earth and the Sun which fixes the upper bound of the mass
of axion as $m_a\lesssim10^{-18}\rm{eV}$. The long range axionic Yukawa
potential between the Earth and Sun changes the gravitational potential between
them and contribute to the light bending and the Shapiro time delay. From the
observational uncertainties of those experiments, we put an upper bound on the
axion decay constant as $f_a\lesssim 9.85\times 10^{6}\rm{GeV}$, which is the
stronger bound obtained from Shapiro time delay. This implies if ALPs are FDM,
then they do not couple to nucleons.
