The Importance of Quantum Pressure of Fuzzy Dark Matter on Lyman-Alpha
  Forest
  With recent Lyman-alpha forest data from BOSS and XQ-100, some studies
suggested that the lower mass limit on the fuzzy dark matter (FDM) particles is
lifted up to $10^{-21}\,\mathrm{eV}$. However, such a limit was obtained by
$\Lambda$CDM simulations with the FDM initial condition and the quantum
pressure (QP) was not taken into account which could have generated non-trivial
effects in large scales structures. We investigate the QP effects in
cosmological simulations systematically, and find that the QP leads to further
suppression of the matter power spectrum at small scales, as well as the halo
mass function in the low mass end. We estimate the suppressing effect of QP in
the 1D flux power spectrum of Lyman-alpha forest and compare it with data from
BOSS and XQ-100. The rough uncertainties of thermal gas properties in the flux
power spectrum model calculation were discussed. We conclude that more
systematic studies, especially with QP taken into account, are necessary to
constrain FDM particle mass using Lyman-alpha forest.
