Axion-like particle dark matter in the linear regime of structure formation

If axion-like particles (ALPs) constitute a major part of dark matter (DM), due to the bosonic nature and a relative small mass, they could behave differently from the point like dark matter particles on the formation of the cosmic structures. When studying the structure formation, it is often useful to consider DM as a special fluid with a given density and a given velocity. ALP fluid obeys a same continuity equation comparing to the point-like collisionless DM but has a different first-order velocity equation. In the linear regime of structure formation, the resulted observational differences are negligible for the QCD axions but can be interesting for very light ALPs.