Scalar Field Dark Matter Research Articles

Comparison between two scalar field models using rotation curves of spiral galaxies

Scalar fields have been used as candidates for dark matter in the universe, from axions with masses ∼ 10-5eV until ultra-light scalar fields with masses ∼ Axions behave as cold dark matter while the ultra-light scalar fields galaxies are Bose-Einstein condensate drops. The ultra-light scalar fields are also called scalar field dark matter model. In this work we study rotation curves for low surface brightness spiral galaxies using two scalar field models: the Gross-Pitaevskii Bose-Einstein condensate in the Thomas-Fermi approximation and a scalar field solution of the Klein-Gordon equation. We also used the zero disk approximation galaxy model where photometric data is not considered, only the scalar field dark matter model contribution to rotation curve is taken into account. From the best-fitting analysis of the galaxy catalog we use, we found the range of values of the fitting parameters: the length scale and the central density. The worst fitting results (values of much greater than 1, on the average) were for the Thomas-Fermi models, i.e., the scalar field dark matter is better than the Thomas- Fermi approximation model to fit the rotation curves of the analysed galaxies. To complete our analysis we compute from the fitting parameters the mass of the scalar field models and two astrophysical quantities of interest, the dynamical dark matter mass within 300 pc and the characteristic central surface density of the dark matter models. We found that the value of the central mass within 300 pc is in agreement with previous reported results, that this mass is ≈ 107 M⊙/pc2, independent of the dark matter model. And, on the contrary, the value of the characteristic central surface density do depend on the dark matter model.

Multistate scalar field dark matter and its correlation with galactic properties

In this paper, we search for the correlations between the intrinsic properties of galaxies and the Bose–Einstein condensate (BEC) under the scheme of a scalar field dark matter (SFDM) at the temperature of condensation greater than zero. According to this paradigm the BEC is distributed in several states. Based on the galactic rotation curves collected in SPARC dataset, we observe that the SFDM parameters present a weak correlation with the most of the galaxy properties, having only a correlation with those related to neutral hydrogen emissions. In addition, we found evidence to the support of self-interaction between the different BEC states proposing that, in future studies, the crossed terms in SFDM equations must be considered. Finally, we find a null correlation with galaxy distances giving support to the nonhierarchy of SFDM formation.

Understanding caustic crossings in giant arcs: Characteristic scales, event rates, and constraints on compact dark matter

The recent discovery of fast transient events near critical curves of massive galaxy clusters, which are interpreted as highly magnified individual stars in giant arcs due to caustic crossing, opens up the possibility of using such microlensing events to constrain a range of dark matter models such as primordial black holes and scalar field dark matter. Based on a simple analytic model, we study lensing properties of a point mass lens embedded in a high magnification region, and derive the dependence of the peak brightness, microlensing time scales, and event rates on the mass of the point mass lens as well as the radius of a source star that is magnified. We find that the lens mass and source radius of the first event MACS J1149 Lensed Star 1 (LS1) are constrained, with the lens mass range of $0.1~M_\odot \lesssim M \lesssim 4\times 10^3M_\odot$ and the source radius range of $40~R_\odot \lesssim R \lesssim 260~R_\odot$. In the most plausible case with $M\approx 0.3~M_\odot$ and $R\approx 180~R_\odot$, the source star should have been magnified by a factor of $\approx 4300$ at the peak. The derived lens properties are fully consistent with the interpretation that MACS J1149 LS1 is a microlensing event produced by a star that contributes to the intra-cluster light. We argue that compact dark matter models with high fractional mass densities for the mass range $10^{-5}M_\odot \lesssim M\lesssim 10^2M_\odot$ are inconsistent with the observation of MACS J1149 LS1 because such models predict too low magnifications. Our work demonstrates a potential use of caustic crossing events in giant arcs to constrain compact dark matter.

Higgs Portal Inflation with Fermionic Dark Matter

We discuss the inflationary model presented in [1], involving a gauge singlet scalar field and fermionic dark matter added to the standard model. Either the Higgs or the singlet scalar could play the role of the inflaton, and slow roll is realized through its non-minimal coupling to gravity. The effective scalar potential is stabilized by the mixing between the scalars as well as the coupling with the fermionic field. Mixing of the two scalars also provides a portal to dark matter. Constraints on the model come from perturbativity and stability, collider searches and dark matter constraints and impose a constraining relationship on the masses of dark matter and scalar fields. Inflationary predictions are generically consistent with current Planck data.

Brief History of Ultra-light Scalar Dark Matter Models

This is a review on the brief history of the scalar field dark matter model also known as fuzzy dark matter, BEC dark matter, wave dark matter, or ultra-light axion. In this model ultra-light scalar dark matter particles with mass m = O(10-22)eV condense in a single Bose-Einstein condensate state and behave collectively like a classical wave. Galactic dark matter halos can be described as a self-gravitating coherent scalar field configuration called boson stars. At the scale larger than galaxies the dark matter acts like cold dark matter, while below the scale quantum pressure from the uncertainty principle suppresses the smaller structure formation so that it can resolve the small scale crisis of the conventional cold dark matter model.

Rotation curves of high-resolution LSB and SPARC galaxies with fuzzy and multistate (ultralight boson) scalar field dark matter

Cold dark matter (CDM) has shown to be an excellent candidate for the dark matter (DM) of the Universe at large scales, however it presents some challenges at the galactic level. The scalar field dark matter (SFDM), also called fuzzy, wave, Bose-Einstein condensate or ultra-light axion DM, is identical to CDM at cosmological scales but different at the galactic ones. SFDM forms core halos, it has a natural cut-off in its matter power spectrum and it predicts well-formed galaxies at high redshifts. In this work we reproduce the rotation curves of high-resolution low surface brightness (LSB) and SPARC galaxies with two SFDM profiles: (1)~The soliton+NFW profile in the fuzzy DM (FDM) model, arising empirically from cosmological simulations of real, non-interacting scalar field (SF) at zero temperature, and (2)~the multistate SFDM (mSFDM) profile, an exact solution to the Einstein-Klein-Gordon equations for a real, self-interacting SF, with finite temperature into the SF potential, introducing several quantum states as a realistic model for a SFDM halo. From the fits with the soliton+NFW profile, we obtained for the boson mass $0.212< m_\psi/(10^{-23} \mathrm{eV}/c^2)<27.0$ and for the core radius $0.326< r_c/\mathrm{kpc}<8.96$. From the combined analysis with the LSB galaxies, we obtained $m_\psi = 0.554 \times10^{-23}\mathrm{eV}$, a result in tension with the severe cosmological constraints. Also, we show the analytical mSFDM model fits the observations as well as or better than the empirical soliton+NFW profile, and it reproduces naturally the wiggles present in some galaxies, being a theoretically motivated framework additional or alternative to the FDM profile.

Scalar field dark matter in hybrid approach

This version matches the one accepted for publication in Physical Review D. There are some minor changes with respect to the previous version

Bose-Einstein-condensed scalar field dark matter and the gravitational wave background from inflation: New cosmological constraints and its detectability by LIGO

We consider an alternative cold dark matter candidate, ultralight bosons ($m>10^{-22}$eV) described by a complex scalar field (SFDM) with global U(1) symmetry, with comoving particle number density conserved after particle production during standard reheating. We allow for repulsive self-interaction. In a Lambda-SFDM universe, SFDM starts relativistic, evolving from stiff (w=1) to radiation-like (w=1/3), becoming nonrelativistic (w=0) at late times. Thus, a stiff-SFDM-dominated era precedes the familiar radiation-dominated era. SFDM particle mass $m$ and quartic self-interaction strength \lambda, are therefore constrained by cosmological observables, N_{eff}, the effective number of neutrino species during BBN, and z_{eq}, the matter-radiation equality redshift. Since the stochastic gravitational wave background (SGWB) from inflation is amplified during the stiff-SFDM-dominated era, it can also contribute a radiationlike component large enough to affect these observables. Remarkably, this amplification makes this SGWB detectable by current GW experiments, e.g., aLIGO/Virgo and LISA, for Lambda-SFDM models satisfying cosmological constraints, for a range of reheat temperatures T_{re} and currently allowed values of tensor-to-scalar ratio $r$. For given r and $\lambda/(mc^2)^2$, the marginally-allowed Lambda-SFDM model for each T_{re} has the smallest m that satisfies cosmological constraints. For example, for marginally-allowed models with r=0.01 and $\lambda/(mc^2)^2=10^{-18}$eV$^{-1}$cm$^3$, null detection by the aLIGO O1 run excludes 8.75*10^3<T_{re} (GeV)<1.7*10^5 at 95% confidence, demonstrating that GW experiments already place a new kind of cosmological constraint on SFDM. A wider parameter range should be accessible to aLIGO/Virgo O5, with potential to detect this signature of Lambda-SFDM. For this same illustrative family, 3-sigma detection is predicted for 600<T_{re} (GeV)<10^7.

Collapse threshold for a cosmological Klein-Gordon field

Oscillating scalar fields are useful to model a variety of matter components in the Universe. One or more scalar fields participate in the reheating process after inflation, while at much lower energies scalar fields are robust dark matter candidates. Pertaining to structure formation in these models, it is well known that inhomogeneities of the Klein-Gordon field are unstable above the characteristic de Broglie wavelength. In this paper we show that such instability implies the existence of a threshold amplitude for the collapse of primordial fluctuations. We use this threshold to correctly predict the cutoff scale of the matter power spectrum in the scalar field dark matter model. Furthermore, for a Klein-Gordon field during reheating we show that this same threshold allows for abundant production of structure (oscillons but not necessarily black holes). Looking at the production of primordial black holes (PBHs) in this scenario we note that the sphericity condition yields a much lower probability of PBH formation at the end of inflation. Remarkably, even after meeting a such stringent condition, we find that PBHs may be overproduced during reheating. We finally constrain the epochs at which an oscillating Klein-Gordon field could dominate the early universe.

Mass discrepancy-acceleration relation: A universal maximum dark matter acceleration and implications for the ultralight scalar dark matter model

Recent analysis of the rotation curves of a large sample of galaxies with very diverse stellar properties reveal a relation between the radial acceleration purely due to the baryonic matter and the one inferred directly from the observed rotation curves. Assuming the dark matter (DM) exists, this acceleration relation is tantamount to an acceleration relation between DM and baryons. This leads us to a universal maximum acceleration for all halos. Using the latter in DM profiles that predict inner cores implies that the central surface density $\mu_{DM} = \rho_s r_s$ must be a universal constant, as suggested by previous studies in selected galaxies, revealing a strong correlation between the density $\rho_s$ and scale $r_s$ parameters in each profile. We then explore the consequences of the constancy of $\mu_{DM}$ in the context of the ultra-light scalar field dark matter model (SFDM). We find that for this model $\mu_{DM} = 648 \, M_\odot {\rm pc}^{-2}$, and that the so-called WaveDM soliton profile should be an universal feature of the DM halos. Comparing with data from the Milky Way and Andromeda satellites, we find that they are consistent with a boson mass of the scalar field particle of the order of $10^{-21} \, {\rm eV}/c^2$, which puts the SFDM model in agreement with recent cosmological constraints.

Galaxy formation with BECDM - I. Turbulence and relaxation of idealized haloes.

We present a theoretical analysis of some unexplored aspects of relaxed Bose-Einstein condensate dark matter (BECDM) haloes. This type of ultralight bosonic scalar field dark matter is a viable alternative to the standard cold dark matter (CDM) paradigm, as it makes the same large-scale predictions as CDM and potentially overcomes CDM's small-scale problems via a galaxy-scale de Broglie wavelength. We simulate BECDM halo formation through mergers, evolved under the Schrödinger-Poisson equations. The formed haloes consist of a soliton core supported against gravitational collapse by the quantum pressure tensor and an asymptotic r-3 NFW-like profile. We find a fundamental relation of the core-to-halo mass with the dimensionless invariant Ξ ≡ |E|/M3/(Gm/ħ)2 or Mc/M ≃ 2.6Ξ1/3, linking the soliton to global halo properties. For r ≥ 3.5 rc core radii, we find equipartition between potential, classical kinetic and quantum gradient energies. The haloes also exhibit a conspicuous turbulent behaviour driven by the continuous reconnection of vortex lines due to wave interference. We analyse the turbulence 1D velocity power spectrum and find a k-1.1 power law. This suggests that the vorticity in BECDM haloes is homogeneous, similar to thermally-driven counterflow BEC systems from condensed matter physics, in contrast to a k-5/3 Kolmogorov power law seen in mechanically-driven quantum systems. The mode where the power spectrum peaks is approximately the soliton width, implying that the soliton-sized granules carry most of the turbulent energy in BECDM haloes.

Scalar field dark matter in clusters of galaxies

One alternative to the cold dark matter (CDM) paradigm is the scalar field dark matter (SFDM) model, which assumes dark matter is a spin-0 ultra-light scalar field (SF) with a typical mass $m\sim10^{-22}\mathrm{eV}/c^2$ and positive self-interactions. Due to the ultra-light boson mass, the SFDM could form Bose-Einstein condensates (BEC) in the very early Universe, which are interpreted as the dark matter haloes. Although cosmologically the model behaves as CDM, they differ at small scales: SFDM naturally predicts fewer satellite haloes, cores in dwarf galaxies and the formation of massive galaxies at high redshifts. The ground state (or BEC) solution at zero temperature suffices to describe low-mass galaxies but fails for larger systems. A possible solution is adding finite-temperature corrections to the SF potential which allows combinations of excited states. In this work, we test the finite-temperature multistate SFDM solution at galaxy cluster scales and compare our results with the Navarro-Frenk-White (NFW) and BEC profiles. We achieve this by fitting the mass distribution of 13 \textit{Chandra} X-ray clusters of galaxies, excluding the region of the brightest cluster galaxy. We show that the SFDM model accurately describes the clusters' DM mass distributions offering an equivalent or better agreement than the NFW profile. The complete disagreement of the BEC model with the data is also shown. We conclude that the theoretically motivated multistate SFDM profile is an interesting alternative to empirical profiles and ad hoc fitting-functions that attempt to couple the asymptotic NFW decline with the inner core in SFDM.

Perturbations of ultralight vector field dark matter

We study the dynamics of cosmological perturbations in models of dark matter based on ultralight coherent vector fields. Very much as for scalar field dark matter, we find two different regimes in the evolution: for modes with {k}^2ll mathrm{mathscr{H}}ma , we have a particle-like behaviour indistinguishable from cold dark matter, whereas for modes with {k}^2gg mathrm{mathscr{H}}ma , we get a wave-like behaviour in which the sound speed is non-vanishing and of order cs2 ≃ k2/m2a2. This implies that, also in these models, structure formation could be suppressed on small scales. However, unlike the scalar case, the fact that the background evolution contains a non-vanishing homogeneous vector field implies that, in general, the evolution of the three kinds of perturbations (scalar, vector and tensor) can no longer be decoupled at the linear level. More specifically, in the particle regime, the three types of perturbations are actually decoupled, whereas in the wave regime, the three vector field perturbations generate one scalar-tensor and two vector-tensor perturbations in the metric. Also in the wave regime, we find that a non-vanishing anisotropic stress is present in the perturbed energy-momentum tensor giving rise to a gravitational slip of order (Φ − Ψ)/Φ ∼ cs2. Moreover in this regime the amplitude of the tensor to scalar ratio of the scalar-tensor modes is also h/Φ ∼ cs2. This implies that small-scale density perturbations are necessarily associated to the presence of gravity waves in this model. We compare their spectrum with the sensitivity of present and future gravity waves detectors.

Spatial solitons in thermo-optical media from the nonlinear Schrödinger-Poisson equation and dark-matter analogs

We analyze theoretically the Schrodinger-Poisson equation in two transverse dimensions in the presence of a Kerr term. The model describes the nonlinear propagation of optical beams in thermooptical media and can be regarded as an analogue system for a self-gravitating self-interacting wave. We compute numerically the family of radially symmetric ground state bright stationary solutions for focusing and defocusing local nonlinearity, keeping in both cases a focusing nonlocal nonlinearity. We also analyze excited states and oscillations induced by fixing the temperature at the borders of the material. We provide simulations of soliton interactions, drawing analogies with the dynamics of galactic cores in the scalar field dark matter scenario.

Can dark matter be a scalar field?

In this paper we study a real scalar field as a possible candidate to explain the dark matter in the universe. In the context of a free scalar field with quadratic potential, we have used Union 2.1 SN Ia observational data jointly with a Planck prior over the dark matter density parameter to set a lower limit on the dark matter mass as m⩾0.12H0−1 eV (c=ℏ=1). For the recent value of the Hubble constant indicated by the Hubble Space Telescope, namely H0=73±1.8 km s−1Mpc−1, this leads to m⩾1.56×10−33 eV at 99.7% c.l. Such value is much smaller than m∼ 10−22 eV previously estimated for some models. Nevertheless, it is still in agreement with them once we have not found evidences for a upper limit on the scalar field dark matter mass from SN Ia analysis. In practice, it confirms free real scalar field as a viable candidate for dark matter in agreement with previous studies in the context of density perturbations, which include scalar field self interaction.

Towards accurate cosmological predictions for rapidly oscillating scalar fields as dark matter

As we are entering the era of precision cosmology, it is necessary to count on accurate cosmological predictions from any proposed model of dark matter. In this paper we present a novel approach to the cosmological evolution of scalar fields that eases their analytic and numerical analysis at the background and at the linear order of perturbations. The new method makes use of appropriate angular variables that simplify the writing of the equations of motion, and which also show that the usual field variables play a secondary role in the cosmological dynamics. We apply the method to a scalar field endowed with a quadratic potential and revisit its properties as dark matter. Some of the results known in the literature are recovered, and a better understanding of the physical properties of the model is provided. It is confirmed that there exists a Jeans wavenumber kJ, directly related to the suppression of linear perturbations at wavenumbers k > kJ, and which is verified to be kJ = a √mH. We also discuss some semi-analytical results that are well satisfied by the full numerical solutions obtained from an amended version of the CMB code CLASS. Finally we draw some of the implications that this new treatment of the equations of motion may have in the prediction of cosmological observables from scalar field dark matter models.

Enabling electroweak baryogenesis through dark matter

We study the impact on electroweak baryogenesis from a swifter cosmological expansion induced by dark matter. We detail the experimental bounds that one can place on models that realize it, and we investigate the modifications of these bounds that result from a non-standard cosmological history. The modifications can be sizeable if the expansion rate of the Universe increases by several orders of magnitude. We illustrate the impact through the example of scalar field dark matter, which can alter the cosmological history enough to enable a strong-enough first-order phase transition in the Standard Model when it is supplemented by a dimension six operator directly modifying the Higgs boson potential. We show that due to the modified cosmological history, electroweak baryogenesis can be realized, while keeping deviations of the triple Higgs coupling below HL-LHC sensitivies. The required scale of new physics to effectuate a strong-enough first order phase transition can change by as much as twenty percent as the expansion rate increases by six orders of magnitude.

Scalar field dark matter and the Higgs field

We discuss the possibility that dark matter corresponds to an oscillating scalar field coupled to the Higgs boson. We argue that the initial field amplitude should generically be of the order of the Hubble parameter during inflation, as a result of its quasi-de Sitter fluctuations. This implies that such a field may account for the present dark matter abundance for masses in the range $10^{-6} - 10^{-4}$ eV, if the tensor-to-scalar ratio is within the range of planned CMB experiments. We show that such mass values can naturally be obtained through either Planck-suppressed non-renormalizable interactions with the Higgs boson or, alternatively, through renormalizable interactions within the Randall-Sundrum scenario, where the dark matter scalar resides in the bulk of the warped extra-dimension and the Higgs is confined to the infrared brane.

Characteristic size and mass of galaxies in the Bose–Einstein condensate dark matter model

We study the characteristic length scale of galactic halos in the Bose-Einstein condensate (or scalar field) dark matter model. Considering the evolution of the density perturbation we show that the average background matter density determines the quantum Jeans mass and hence the spatial size of galaxies at a given epoch. In this model the minimum size of galaxies increases while the minimum mass of the galaxies decreases as the universe expands. The observed values of the mass and the size of the dwarf galaxies are successfully reproduced with the dark matter particle mass $m\simeq 5\times 10^{-22}eV$. The minimum size is about $6\times 10^{-3}\sqrt{m/H}\lambda_c$ and the typical rotation velocity of the dwarf galaxies is $O(\sqrt{H/m}$) c, where $H$ is the Hubble parameter and $\lambda_c$ is the Compton wave length of the particle. We also suggest that ultra compact dwarf galaxies are the remnants of the dwarf galaxies formed in the early universe.

Scalar dark matter in light of LEP and proposed ILC experiments

In this work we study a scalar field dark matter model with mass of the order of 100 MeV. We assume dark matter is produced in the process $e^-+e^+\to \phi +\phi^*+\gamma$, that, in fact, could be a background for the standard process $e^-+e^+\to \nu +\bar\nu+\gamma$ extensively studied at LEP. We constrain the chiral couplings, $C_L$ and $C_R$, of the dark matter with electrons through an intermediate fermion of mass $m_F=100$ GeV and obtain $C_L=0.1(0.25)$ and $C_R=0.25(0.1)$ for the best fit point of our $\chi^2$ analysis. We also analyze the potential of ILC to detect this scalar dark matter for two configurations: (i) center of mass energy $\sqrt{s}=500$ GeV and luminosity $\mathcal{L}=250$ fb$^{-1}$, and (ii) center of mass energy $\sqrt{s}=1$ TeV and luminosity $\mathcal{L}=500$ fb$^{-1}$. The differences of polarized beams are also explored to better study the chiral couplings.