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.
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