Non-relativistic approach for cosmological Scalar Field Dark Matter

Understand

We derive non-relativistic equations of motion for the formation of cosmological structure in a Scalar Field Dark Matter (SFDM) model corresponding to a complex scalar field endowed with a quadratic scalar potential.

• Starting with the full equations of motion written in the Newtonian gauge of scalar perturbations, we separate out the fields involved into relativistic and non-relativistic parts, and find the equations of motion for the latter that can be used to build up the full solution.
• One important assumption will also be that the SFDM field is in the regime of fast oscillations, under which its behavior is exactly that of cold dark matter.
• The resultant equations are quite similar to the Schr\"odinger-Poisson system of Newtonian boson stars plus relativistic leftovers.