Quantum Statistical Effects on Warm Dark Matter and the Mass Constraint from the Cosmic Structure at Small Scales

The suppression of the small-scale matter power spectrum is a distinct feature of Warm Dark Matter (WDM), which permits a constraint on the WDM mass from galaxy surveys. In the thermal relic WDM scenario, quantum statistical effects are not manifest. In a unified framework, we investigate the quantum statistical effects for a fermion case with a degenerate pressure and a boson case with a Bose-Einstein condensation (BEC). Compared to the thermal relic case, the degenerate fermion case only slightly lowers the mass bound, while the boson case with a high initial BEC fraction ($\gtrsim 90\mathrm{\%}$) significantly lowers it. On the other hand, the BEC fraction drops during the relativistic-to-nonrelativistic transition and completely disappears if the initial fraction is below $\sim 64$%. Given the rising interest in resolving the late-time galaxy-scale problems with boson condensation, a question is posed on how a high initial BEC fraction can be dynamically created so that a condensed DM component remains today.