Non-relativistic approach for cosmological Scalar Field Dark Matter

Abstract

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 Schrödinger-Poisson system of Newtonian boson stars plus relativistic leftovers. We exploit that similarity to show how to simulate, with minimum numerical effort, the formation of cosmological structure in SFDM models and others alike, and ultimately prove their viability as complete dark matter models.

RevTex file, 5 pages, no figures. Matches published version in Physical Review D

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Cited by in corpus (14)

• Towards accurate cosmological predictions for rapidly oscillating scalar fields as dark matter
• Sourcing Dark Matter and Dark Energy from $\alpha$-attractors
• Cosmological nonlinear structure formation in full general relativity
• Rotation curves of ultralight BEC dark matter halos with rotation
• Cosmological scalar field perturbations can grow
• Scalar Field as a Bose-Einstein Condensate?
• Gravitational Waves from Axion Monodromy
• Scalar field dark matter with a cosh potential, revisited
• Space-Time Curvature Signatures in Bose-Einstein Condensates
• The Schr$\ddot{o}$dinger-Poisson equations as the large-N limit of the Newtonian N-body system: applications to the large scale dark matter dynamics
• Scalar field as a Bose-Einstein condensate in a Schwarzschild-de Sitter spacetime
• Nonlinear cosmological structure with ultralight bosons via modified gravity
• Non-relativistic Limit of Thermodynamics of Bose Field in a Static Space-time and Bose-Einstein Condensation
• Oscillating scalar field as dark matter through the cosmological epochs