Growth of perturbations in an expanding universe with Bose-Einstein condensate dark matter

Abstract

We study the growth of perturbations in an expanding Newtonian universe with Bose-Einstein condensate (BEC) dark matter. We first ignore special relativistic effects and derive a differential equation that governs the evolution of the density contrast in the linear regime. This equation, which takes quantum pressure and self-interaction into account, can be solved analytically in several cases. We argue that an attractive self-interaction can enhance the Jeans instability and fasten the formation of structures. Then, we take pressure effects (coming from special relativity) into account in the evolution of the cosmic fluid and add the contribution of radiation, baryons, and dark energy (cosmological constant). For BEC dark matter with repulsive self-interaction (positive pressure) the scale factor increases more rapidly than in the standard ΛCDM model where dark matter is pressureless, while it increases less rapidly for BEC dark matter with attractive self-interaction (negative pressure). We study the linear development of the perturbations in these two cases and show that the perturbations grow faster in BEC dark matter than in pressureless dark matter. Finally, we consider a "dark fluid" with a generalized equation of state p = (αρ + kρ 2 )c 2 having a component p = kρ 2 c 2 similar to BEC dark matter and a component p = αρc 2 mimicking the effect of the cosmological constant (dark energy). We find optimal parameters that give good agreement with the standard ΛCDM model that assumes a finite cosmological constant.

Hydrodynamic representation of a cosmic scalar field

“…5 Expanding the solutions of Eq. (25) in Fourier modes of the form δ( x, t) = δ k (t)e i k· x , we obtain…”

A Review on the Scalar Field/Bose-Einstein Condensate Dark Matter Model

“…For example, [55] proposed fuzzy dark matter composed of ultra-light scalar particles initially in the form of a BEC. Recently [50,52] developed a further analysis of the cosmological dynamics of SFDM/BEC as well as the evolution of their fluctuations (see also [26]). In the same direction, [114,76] studied the growth of scalar fluctuations and the formations of large-scale structure within a fluid and a field approach for the SFDM/BEC model.…”

Cosmological perturbations in coherent oscillating scalar field models

“…This subject has been mainly JHEP03(2016)013 studied for harmonic potential models that mimic the standard dark matter case [65][66][67][68][69][70][71], as it happens for the axion field [72,73]. It has been proved by using the linear perturbation theory that the axion was equivalent to CDM for high enough masses [74][75][76][77].…”