Despite the great successes of the Cold Dark Matter (CDM) model in explaining a wide range of observations of the global evolution and the formation of galaxies and large-scale structure in the Universe, the origin and microscopic nature of dark matter is still unknown. The most common form of CDM considered to-date is that of Weakly Interacting Massive Particles (WIMPs), but, so far, attempts to detect WIMPs directly or indirectly have not yet succeeded, and the allowed range of particle parameters has been significantly restricted. Some of the cosmological predictions for this kind of CDM are even in apparent conflict with observations (e.g. cuspy-cored halos and an overabundance of satellite dwarf galaxies). For these reasons, it is important to consider the consequences of different forms of CDM. We focus here on the hypothesis that the dark matter is comprised, instead, of ultralight bosons that form a Bose-Einstein Condensate, described by a complex scalar field, for which particle number per unit comoving volume is conserved. We start from the Klein-Gordon and Einstein field equations to describe the evolution of the Friedmann-RobertsonWalker universe in the presence of this kind of dark matter. We find that, in addition to the radiation-, matter-, and Λ-dominated phases familiar from the standard CDM model, there is an earlier phase of scalar-field-domination, which is special to this model. In addition, while WIMP CDM is nonrelativistic at all times after it decouples, the equation of state of Bose-Einistein condensed scalar field dark matter (SFDM) is found to be relativistic at early times, evolving from stiff (p =ρ) to radiationlike (p =ρ/3), before it becomes non-relativistic and CDM-like at late times (p = 0). The timing of the transitions between these phases and regimes is shown to yield fundamental constraints on the SFDM model parameters, particle mass m and self-interaction coupling strength λ. We show that SFDM is compatible with observations of the evolving background universe, by deriving the range of particle parameters required to match observations of the cosmic microwave background (CMB) and the abundances of the light elements produced by big bang nucleosynthesis (BBN), including N eff , the effective number of neutrino species, and the epoch of matter-radiation equality zeq. This yields m ≥ 2.4 × 10 −21 eV/c 2 and 9.5 × 10 −19 eV −1 cm 3 ≤ λ/(mc 2 ) 2 ≤ 4 × 10 −17 eV −1 cm 3 . Indeed, our model can accommodate current observations in which N eff is higher at the BBN epoch than at zeq, probed by the CMB, which is otherwise unexplained by the standard CDM model involving WIMPs. We also show that SFDM without self-interaction (also called "fuzzy dark matter") is not able to comply with the current constraints from BBN within 68% confidence, and is therefore disfavored.PACS numbers: 98.80. 95.35.+d, 98.80.Cq, 98.80.Ft

Various extensions of the standard model of particle physics predict the existence of very light bosons, with masses ranging from about 10 −5 eV for the QCD axion down to 10 −33 eV for ultra-light particles. These particles could be responsible for all or part of the cold dark matter (CDM) in the Universe. For such particles to serve as CDM, their phase-space density must be high enough to form a Bose-Einstein condensate (BEC). The fluid-like nature of BEC-CDM dynamics differs from that of standard collisionless CDM, however, so different signature effects on galactic haloes may allow observations to distinguish them. Standard CDM has problems with galaxy observations on small scales; cuspy central density profiles of haloes and the overabundance of subhaloes seem to conflict with observations of dwarf galaxies. It has been suggested that BEC-CDM can overcome these shortcomings for a large range of particle mass m and self-interaction coupling strength g. For quantum coherence to influence structure on the scale of galactic haloes of radius R and mass M, either the de-Broglie wavelength λ deB R, which requires m m H ∼ = 10 −25 (R/100 kpc) −1/2 (M/10 12 M ) −1/2 eV, or else λ deB R but gravity is balanced by self-interaction, which requires m m H and g g H ∼ = 2 × 10 −64 (R/100 kpc)(M/10 12 M ) −1 eV cm 3 . Here we study the largely neglected effects of angular momentum on BEC haloes. Dimensionless spin parameters λ 0.05 are expected from tidal-torquing by large-scale structure formation, just as for standard CDM. Since laboratory BECs develop quantum vortices if rotated rapidly enough, we ask whether this amount of angular momentum is sufficient to form vortices in BEC haloes, which would affect their structure with potentially observable consequences. The minimum angular momentum required for a halo to sustain a vortex, L QM , corresponds to per particle, or M/m. For λ = 0.05, this requires m ≥ 9.5m H , close enough to the particle mass required to influence structure on galactic scales that BEC haloes may be subject to vortex formation. While this is a necessary condition, it is not sufficient. To determine if and when quantum vortices will form in BEC haloes with a given λ-value, we study the equilibrium of self-gravitating, rotating, virialized BEC haloes which satisfy the Gross-Pitaevskii-Poisson equations, and calculate under what conditions vortices are energetically favoured, in two limits: either just enough angular momentum for one vortex or a significant excess of angular momentum. For λ = 0.05, vortex formation is energetically favoured for L/L QM ≥ 1 as long as both m/m H ≥ 9.5 and g/g H ≥ 68.0. Hence, vortices are expected for a wide range of BEC parameters. However, vortices cannot form for vanishing self-interaction (i.e. when λ deB R), and a range of particle parameters also remain even for BEC haloes supported by self-interaction, for which vortices will not form. Such BEC haloes can be modelled by compressible, (n = 1)-polytropic, irrotational Riemann-S ellipsoids.

Scalar Field Dark Matter (SFDM) comprised of ultralight bosons has attracted great interest as an alternative to standard, collisionless Cold Dark Matter (CDM) because of its novel structure-formation dynamics, described by the coupled Schrödinger-Poisson equations. In the free-field (“fuzzy”) limit of SFDM (FDM), structure is inhibited below the de Broglie wavelength, but resembles CDM on larger scales. Virialized haloes have “solitonic” cores of radius ∼λdeB, surrounded by CDM-like envelopes. When a strong enough repulsive self-interaction (SI) is also present, structure can be inhibited below a second length scale, λSI, with λSI > λdeB called the Thomas-Fermi (TF) regime. FDM dynamics differs from CDM because of quantum pressure, and SFDM-TF differs further by adding SI pressure. In the small-λdeB limit, however, we can model all three by fluid conservation equations for a compressible, γ = 5/3 ideal gas, with ideal gas pressure sourced by internal velocity dispersion and, for the TF regime, an added SI pressure, PSI∝ρ2. We use these fluid equations to simulate halo formation from gravitational collapse in 1D, spherical symmetry, demonstrating for the first time that SFDM-TF haloes form with cores the size of RTF, the radius of an SI-pressure-supported (n = 1)-polytrope, surrounded by CDM-like envelopes. In comparison with rotation curves of dwarf galaxies in the local Universe, SFDM-TF haloes pass the [“too-big-to-fail” + “core-cusp”]-test if RTF ≳ 1 kpc.

We study a rotating Bose-Einstein condensate in a strongly anharmonic trap ͑flat trap with a finite radius͒ in the framework of two-dimensional Gross-Pitaevskii theory. We write the coupling constant for the interactions between the gas atoms as 1/ 2 and we are interested in the limit → 0 ͑Thomas-Fermi limit͒ with the angular velocity ⍀ depending on . We derive rigorously the leading asymptotics of the ground state energy and the density profile when ⍀ tends to infinity as a power of 1/. If ⍀͑͒ = ⍀ 0 / a "hole" ͑i.e., a region where the density becomes exponentially small as 1 / → ϱ͒ develops for ⍀ 0 above a certain critical value. If ⍀͑͒ ӷ 1/ the hole essentially exhausts the container and a "giant vortex" develops with the density concentrated in a thin layer at the boundary. While we do not analyze the detailed vortex structure we prove that rotational symmetry is broken in the ground state for const͉log ͉ Ͻ⍀͑͒ Շ const/ .

The nature of the cosmological dark matter remains elusive. Recent studies have advocated the possibility that dark matter could be composed of ultra-light, self-interacting bosons, forming a Bose-Einstein condensate in the very early Universe. We consider models which are charged under a global U (1)-symmetry such that the dark matter number is conserved. It can then be described as a classical complex scalar field which evolves in an expanding Universe. We present a brief review on the bounds on the model parameters from cosmological and galactic observations, along with the properties of galactic halos which result from such a dark matter candidate.