Cosmological perturbations for ultra-light axion-like particles in a state of Bose-Einstein condensate

Understand

For ultra-light scalar particles like axions, dark matter can form a state of the Bose-Einstein condensate (BEC) with a coherent classical wave whose wavelength is of order galactic scales.

• In the context of an oscillating scalar field with mass $m$, this BEC description amounts to integrating out the field oscillations over the Hubble time scale $H^{-1}$ in the regime $m \gg H$.
• We provide a gauge-invariant general relativistic framework for studying cosmological perturbations in the presence of a self-interacting BEC associated with a complex scalar field.
• In particular, we explicitly show the difference of BECs from perfect fluids by taking into account cold dark matter, baryons, and radiation as a Schutz-Sorkin description of perfect fluids.