Fuzzy Dark Matter Research Articles

Analytical approach to the core-halo structure of fuzzy dark matter

Ultralight bosonic dark matter called fuzzy dark matter (FDM) has attracted much attention as an alternative to the cold dark matter. An intriguing feature of the FDM model is the presence of a soliton core, a stable dense core formed at the center of halos. In this paper, we analytically study the dependence of the soliton core properties on the halo characteristics by solving approximately the Schr\"odinger-Poisson equation. Focusing on the ground-state eigenfunction, we derive a key expression for the soliton core radius, from which we obtain the core-halo mass relations similar to those found in the early numerical work, but involving the factor dependent crucially on the halo concentration and cosmological parameters. Based on the new relations, we find that for a given cosmology, (i) there exist a theoretical bound on the radius and mass of soliton core for each halo mass (ii) incorporating the concentration-halo mass (C-M) relation into the predictions, the core-halo relations generally exhibit a non power-law behavior, and with the C-M relation suppressed at the low-mass scales, relevant to the FDM model, predictions tend to match the simulations well (iii) the scatter in the C-M relation produces a sizable dispersion in the core-halo relations, and can explain the results obtained from cosmological simulations. Finally, the validity of our analytical treatment are critically examined. A perturbative estimation suggests that the prediction of the core-halo relations is valid over a wide range of parameter space, and the impact of the approximation invoked in the analytical calculations is small, although it is not entirely negligible.

Black Hole in Quantum Wave Dark Matter

AbstractIn this work, we explored the effect of the fuzzy dark matter (FDM) (or wave dark matter) halo on a supermassive black hole (SMBH). Such a dark matter introduces a soliton core density profile, and we treat it ideally as a spherical distribution that surrounds the SMBH located at its center. In this direction, we obtained a new metric due to the union of the black hole and dark matter spacetime geometries. We applied the solution to the two known SMBH ‐ Sgr. A* and M87* and used the empirical data for the shadow diameter by EHT to constrain the soliton core radius given some values of the boson mass . Then, we examine the behavior of the shadow radius based on such constraints and relative to a static observer. We found that different shadow sizes are perceived at regions and , and the deviation is greater for values eV. Concerning the shadow behavior, we have also analyzed the effect of the soliton profile on the thin‐accretion disk. Soliton dark matter effects manifest through the varying luminosity near the event horizon. We also analyzed the weak deflection angle and the produced Einstein rings due to soliton effects. We found considerable deviation, better than the shadow size deviation, for the light source near the SMBH with impact parameters comparable to the soliton core. Our results suggest the possible experimental detection of soliton dark matter effects using an SMBH at the galactic centers.

Exploration of simple scenarios involving fuzzy dark matter cores and gas at local scales

ABSTRACT We introduce a tool that solves the Schrödinger–Euler–Poisson system of equations and allows the study of the interaction between ultralight bosonic dark matter, whose dynamics is described with the Schrödinger–Poisson system and luminous matter which, as a first approximation, is modelled with a single component compressible ideal fluid. The two matter fields are coupled through the Poisson equation, whose source is the addition of both, dark matter and fluid densities. We describe the numerical methods used to solve the system of equations and present tests for each of the two components, which show the accuracy and convergence properties of the code. As simple possible applications we present some toy scenarios: (i) the merger between a core of dark matter with a cloud of gas, (ii) the merger of bosonic dark matter plus fluid configurations, and (iii) the post-merger properties, including the dark matter offset from gas and the correlation between oscillations of the bosonic core and those of the gas.

Can ultralight dark matter explain the age–velocity dispersion relation of the Milky Way disc: A revised and improved treatment

ABSTRACT Ultralight axion-like particles ma ∼ 10−22 eV, or Fuzzy Dark Matter (FDM), behave comparably to cold dark matter (CDM) on cosmological scales and exhibit a kpc-size de Broglie wavelength capable of alleviating established (sub-)galactic-scale problems of CDM. Substructures inside an FDM halo incur gravitational potential perturbations, resulting in stellar heating sufficient to account for the Galactic disc thickening over a Hubble time, as first demonstrated by Church et al. We present a more sophisticated treatment that incorporates the full baryon and dark matter distributions of the Milky Way and adopts stellar disc kinematics inferred from recent Gaia, APOGEE, and LAMOST surveys. Ubiquitous density granulation and subhalo passages, respectively, drive inner disc thickening and flaring of the outer disc, resulting in an observationally consistent ‘U-shaped’ disc vertical velocity dispersion profile with the global minimum located near the solar radius. The observed age–velocity dispersion relation in the solar vicinity can be explained by the FDM-substructure-induced heating and places an exclusion bound ma ≳ 0.4 × 10−22 eV. We assess non-trivial uncertainties in the empirical core–halo relation, FDM subhalo mass function and tidal stripping, and stellar heating estimate. The mass range ma ≃ 0.5–0.7 × 10−22 eV favoured by the observed thick disc kinematics is in tension with several exclusion bounds inferred from dwarf density profiles, stellar streams, and Milky Way satellite populations, which could be significantly relaxed due to the aforesaid uncertainties. Additionally, strongly anisotropic heating could help explain the formation of ultra-thin disc galaxies.

Astroparticle Constraints from the Cosmic Star Formation Rate Density at High Redshift: Current Status and Forecasts for JWST

We exploit the recent determination of the cosmic star formation rate (SFR) density at high redshifts z≳4 to derive astroparticle constraints on three common dark matter (DM) scenarios alternative to standard cold dark matter (CDM): warm dark matter (WDM), fuzzy dark matter (ψDM) and self-interacting dark matter (SIDM). Our analysis relies on the ultraviolet (UV) luminosity functions measured from blank field surveys by the Hubble Space Telescope out to z≲10 and down to UV magnitudes MUV≲−17. We extrapolate these to fainter yet unexplored magnitude ranges and perform abundance matching with the halo mass functions in a given DM scenario, thus, obtaining a redshift-dependent relationship between the UV magnitude and the halo mass. We then computed the cosmic SFR density by integrating the extrapolated UV luminosity functions down to a faint magnitude limit MUVlim, which is determined via the above abundance matching relationship by two free parameters: the minimum threshold halo mass MHGF for galaxy formation, and the astroparticle quantity X characterizing each DM scenario (namely, particle mass for WDM and ψDM, and kinetic temperature at decoupling TX for SIDM). We perform Bayesian inference on such parameters using a Monte Carlo Markov Chain (MCMC) technique by comparing the cosmic SFR density from our approach to the current observational estimates at z≳4, constraining the WDM particle mass to mX≈1.2−0.4(−0.5)+0.3(11.3) keV, the ψDM particle mass to mX≈3.7−0.4(−0.5)+1.8(+12.9.3)×10−22 eV, and the SIDM temperature to TX≈0.21−0.06(−0.07)+0.04(+1.8) keV at 68% (95%) confidence level. Finally, we forecast how such constraints will be strengthened by upcoming refined estimates of the cosmic SFR density if the early data on the UV luminosity function at z≳10 from the James Webb Space Telescope (JWST) will be confirmed down to ultra-faint magnitudes.

Constraining ultralight vector dark matter with the Parkes Pulsar Timing Array second data release

Composed of ultralight bosons, fuzzy dark matter provides an intriguing solution to challenges that the standard cold dark matter model encounters on sub-galactic scales. The ultralight dark matter with mass $m\sim10^{-23} \rm{eV}$ will induce a periodic oscillation in gravitational potentials with a frequency in the nanohertz band, leading to observable effects in the arrival times of radio pulses from pulsars. Unlike scalar dark matter, pulsar timing signals induced by the vector dark matter are dependent on the oscillation direction of the vector fields. In this work, we search for ultralight vector dark matter in the mass range of $[2\times 10^{-24}, 2\times 10^{-22}]{\rm{eV}}$ through its gravitational effect in the Parkes Pulsar Timing Array (PPTA) second data release. Since no statistically significant detection is made, we place $95\%$ upper limits on the local dark matter density as $\rho_{\rm{\tiny{VF}}} \lesssim 5{\rm{GeV/cm^{3}}}$ for $m\lesssim 10^{-23}{\rm{eV}}$. As no preferred direction is found for the vector dark matter, these constraints are comparable to those given by the scalar dark matter search with an earlier 12-year data set of PPTA.

New logotropic model based on a complex scalar field with a logarithmic potential

We introduce a new logotropic model based on a complex scalar field with a logarithmic potential that unifies dark matter and dark energy. The scalar field satisfies a nonlinear wave equation generalizing the Klein-Gordon equation in the relativistic regime and the Schr\"odinger equation in the nonrelativistic regime. This model has an intrinsically quantum nature and returns the $\Lambda$CDM model in the classical limit $\hbar\rightarrow 0$. It involves a new fundamental constant of physics $A/c^2=2.10\times 10^{-26}\, {\rm g}\, {\rm m}^{-3}$ responsible for the late accelerating expansion of the Universe and superseding the Einstein cosmological constant $\Lambda$. The logotropic model is almost indistinguishable from the $\Lambda$CDM model at large (cosmological) scales but solves the CDM crisis at small (galactic) scales. It also solves the problems of the fuzzy dark matter model. Indeed, it leads to cored dark matter halos with a universal surface density $\Sigma_0^{\rm th}=5.85\,\left ({A}/{4\pi G}\right )^{1/2}=133\, M_{\odot}/{\rm pc}^2$. This universal surface density is predicted from the logotropic model without adjustable parameter and turns out to be close to the observed value $\Sigma_0^{\rm obs}=141_{-52}^{+83}\, M_{\odot}/{\rm pc}^2$. We also argue that the quantities $\Omega_{\rm dm,0}$ and $\Omega_{\rm de,0}$, which are usually interpreted as the present proportion of dark matter and dark energy in the $\Lambda$CDM model, are equal to $\Omega_{\rm dm,0}^{\rm th}=\frac{1}{1+e}(1-\Omega_{\rm b,0})=0.2559$ and $\Omega_{\rm de,0}^{\rm th}=\frac{e}{1+e}(1-\Omega_{\rm b,0})=0.6955$ in very good agreement with the measured values $\Omega_{\rm dm,0}^{\rm obs}=0.2589$ and $\Omega_{\rm de,0}^{\rm obs}=0.6911$ (their ratio $2.669$ is close to the pure number $e=2.71828...$).

Excluding fuzzy dark matter with sizes and stellar kinematics of ultrafaint dwarf galaxies

We use observations of ultrafaint dwarf (UFD) galaxies to constrain the particle mass of ultralight dark matter. Potential fluctuations created by wave interference in virialized ``fuzzy'' dark matter (FDM) halos dynamically heat stellar orbits in UFDs, some of which exhibit velocity dispersions of $\ensuremath{\lesssim}3\text{ }\text{ }\mathrm{km}/\mathrm{s}$ and sizes $\ensuremath{\lesssim}40\text{ }\text{ }\mathrm{pc}$. Using simulations of FDM halos, and existing measurements of sizes and stellar radial velocities in Segue 1 and Segue 2 UFDs, we derive a lower limit on the dark matter particle mass of ${m}_{\mathrm{FDM}}>3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}\text{ }\text{ }\mathrm{eV}$ at 99% confidence, marginalized over host halo circular velocity. This constraint is conservative as it is derived under the assumption that soliton heating is negligible, and that no other sources of non-FDM dynamical heating of stars operate to increase velocity dispersion. It can potentially be strengthened by future spectroscopic observations of additional stars in ultrafaint galaxies and by tightening theoretical constraints on the soliton size-halo mass relation. However, even the current conservative lower limit on the ultralight dark matter mass makes it indistinguishable from cold dark matter at the scales probed by existing astronomical observations.

Viability of ultralight bosonic dark matter in dwarf galaxies

The dark matter distribution in dwarf galaxies holds a wealth of information on the fundamental properties and interactions of the dark matter particle. In this paper, we study whether ultralight bosonic dark matter is consistent with the gravitational potential extracted from stellar kinematics. We use velocity dispersion measurements to constrain models for halo mass and particle mass. The posterior likelihood is multimodal. Particle masses of order $m\sim 10^{-22} {\rm{eV}}$ require halos of mass in excess of $\sim 10^{10} M_\odot$, while particle mass of order $m \gtrsim 10^{-20}{\rm{eV}}$ are favored by halos of mass $\sim [10^{8} - 10^{9}] M_\odot$, with a similar behavior to cold dark matter. Regardless of particle mass, the lower halo masses are allowed if stellar dynamics are influenced by the presence of a central black hole of mass at most $\sim 10^{-2}$ the host halo mass. We find no preference for models that contain a black hole over models that do not contain a black hole. Our main conclusion is that either the fuzzy dark matter particle mass must be $m \gtrsim 10^{-20}$ eV, or the Milky Way dwarfs must be unusually heavy given the expected hierarchical assembly of the Milky Way, or the Milky Way dwarfs must contain a central black hole. We find no evidence for either of the last two possibilities and consider them unlikely.

Astroparticle Constraints from Cosmic Reionization and Primordial Galaxy Formation

We derived astroparticle constraints in different dark matter scenarios that are alternatives to cold dark matter (CDM): thermal relic warm dark matter, WDM; fuzzy dark matter, ψDM; self-interacting dark matter, SIDM; sterile neutrino dark matter, νDM. Our framework is based on updated determinations of the high-redshift UV luminosity functions for primordial galaxies to redshift z∼10, on redshift-dependent halo mass functions in the above DM scenarios from numerical simulations, and on robust constraints on the reionization history of the Universe from recent astrophysical and cosmological datasets. First, we built an empirical model of cosmic reionization characterized by two parameters, namely the escape fraction fesc of ionizing photons from primordial galaxies, and the limiting UV magnitude MUVlim down to which the extrapolated UV luminosity functions steeply increased. Second, we performed standard abundance matching of the UV luminosity function and the halo mass function, obtaining a relationship between UV luminosity and the halo mass, whose shape depends on an astroparticle quantity X specific to each DM scenario (e.g., WDM particle mass); we exploited such a relationship to introduce (in the analysis) a constraint from primordial galaxy formation, in terms of the threshold halo mass above which primordial galaxies can efficiently form stars. Third, we performed Bayesian inference on the three parameters fesc, MUVlim, and X via a standard MCMC technique, and compared the outcomes of different DM scenarios on the reionization history. We also investigated the robustness of our findings against educated variations of still uncertain astrophysical quantities. Finally, we highlight the relevance of our astroparticle estimates in predicting the behavior of the high-redshift UV luminosity function at faint, yet unexplored magnitudes, which may be tested with the advent of the James Webb Space Telescope.

Closing the window on fuzzy dark matter with the 21-cm signal

Fuzzy dark matter (FDM) is a well-motivated candidate for dark matter (DM) as its tiny mass and large de-Broglie wavelength suppress small-scale matter fluctuations, thereby solving some of the small-scale discrepancies in $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$. Although it has been ruled out as the single component of DM by several observables, there is still a region in the FDM parameter space (the ``FDM window,'' ${10}^{\ensuremath{-}25}\text{ }\text{ }\mathrm{eV}\ensuremath{\lesssim}{m}_{\mathrm{FDM}}\ensuremath{\lesssim}\phantom{\rule{0ex}{0ex}}{10}^{\ensuremath{-}23}\text{ }\text{ }\mathrm{eV}$) where FDM is allowed to comprise a large portion of the total DM. In this work, for the first time, we study the signature of FDM (comprised of ultralight axions) in fractions less than unity on the 21-cm signal and its detectability by 21-cm interferometers such as HERA, taking into account the degeneracy with both astrophysical and cosmological parameters, using a new pipeline that combines modified versions of the camb and 21-cmfast codes. Our forecasts imply that HERA in its design performance will be sensitive to FDM fractions as small as 1% in the FDM window, and improve over existing bounds for other masses by up to an order of magnitude.

Amplitude and phase fluctuations of gravitational waves magnified by strong gravitational lensing

We discuss how small-scale density perturbations on the Fresnel scale affect amplitudes and phases of gravitational waves that are magnified by gravitational lensing in geometric optics. We derive equations that connect the small-scale density perturbations with the amplitude and phase fluctuations to show that such perturbative wave optics effects are significantly boosted in the presence of macro model magnifications such that amplitude and phase fluctuations can easily be observed for highly magnified gravitational waves. We discuss expected signals due to microlensing by stars, dark matter substructure, fuzzy dark matter, and primordial black holes.

Subsonic accretion and dynamical friction for a black hole moving through a self-interacting scalar dark matter cloud

We investigate the flow around a black hole moving through a cloud of self-interacting scalar dark matter. We focus on the large scalar mass limit, with quartic self-interactions, and on the subsonic regime. We show how the scalar field behaves as a perfect gas of adiabatic index $\gamma_{\rm ad}=2$ at large radii while the accretion rate is governed by the relativistic regime close to the Schwarzschild radius. We obtain analytical results thanks to large-radius expansions, which are also related to the small-scale relativistic accretion rate. We find that the accretion rate is greater than for collisionless particles, by a factor $c/c_s \gg 1$, but smaller than for a perfect gas, by a factor $c_s/c \ll 1$, where $c_s$ is the speed of sound. The dynamical friction is smaller than for a perfect gas, by the same factor $c_s/c \ll 1$, and also smaller than Chandrasekhar's result for collisionless particles, by a factor $c_s/(cC)$, where $C$ is the Coulomb logarithm. It is also smaller than for fuzzy dark matter, by a factor $v_0/c \ll 1$.

Fuzzy dark matter and the Dark Energy Survey Year 1 data

ABSTRACT Gravitational weak lensing by dark matter haloes leads to a measurable imprint in the shear correlation function of galaxies. Fuzzy dark matter (FDM), composed of ultralight axion-like particles of mass m ∼ 10−22 eV, suppresses the matter power spectrum and shear correlation with respect to standard cold dark matter. We model the effect of FDM on cosmic shear using the optimized halo model HMCode, accounting for additional suppression of the mass function and halo concentration in FDM as observed in N-body simulations. We combine Dark Energy Survey Year 1 (DES-Y1) data with the Planck cosmic microwave background anisotropies to search for shear correlation suppression caused by FDM. We find no evidence of suppression compared to the preferred cold dark matter model, and thus set a new lower limit to the FDM particle mass. Using a log-flat prior and marginalizing over uncertainties related to the non-linear model of FDM, we find a new, independent 95 per cent C.L. lower limit log10m > −23 combining Planck and DES-Y1 shear, an improvement of almost two orders of magnitude on the mass bound relative to CMB-only constraints. Our analysis is largely independent of baryonic modelling, and of previous limits to FDM covering this mass range. Our analysis highlights the most important aspects of the FDM non-linear model for future investigation. The limit to FDM from weak lensing could be improved by up to three orders of magnitude with $\mathcal {O}(0.1)$ arcmin cosmic shear angular resolution, if FDM and baryonic feedback can be simultaneously modelled to high precision in the halo model.

Cosmological structure formation in complex scalar field dark matter versus real ultralight axions: A comparative study using class

(abridged) We continue the study of $\Lambda$SFDM cosmologies, which differ from $\Lambda$CDM in that CDM is replaced by scalar field dark matter (SFDM) by calculating the evolution of the background Universe, as well as linear perturbations, focusing on scalar modes. We consider models with complex scalar field with a repulsive, quartic self-interaction (SI), and models without SI, referred to as fuzzy dark matter (FDM). To this end, we modify the Boltzmann code CLASS, to incorporate the physics of complex SFDM which has as one of its characteristics that its equation of state is maximally stiff in the very early Universe, dominating then over all the other cosmic components, even over radiation. We calculate CMB and matter power spectra as well as unconditional Press-Schechter halo mass functions for various models, expanding previous literature that were limited either to the background, or to a semi-analytical approach to SFDM density perturbations neglecting the early stiff phase. Comparing our results of each, SFDM and FDM, with real-field ultralight axion models (ULAs) without SI, we characterize the differences between the respective background evolution and linear structure growth. Our calculations confirm previous results of recent literature, implying that SFDM models with $\gtrsim$ kpc-size halo cores are disfavored, questioning their ability to explain the small-scale problems on dwarf-galactic scales. Also we find that the kinetic energy due to the phase of the complex field leads to marked differences between SFDM/FDM versus ULAs. The mild falloff in the SFDM power spectrum toward high k is similar to that of CDM but based on different effects, namely the rapidly shrinking Jeans mass for SFDM as opposed to the Meszaros effect for CDM. In addition, we find that the sharp cutoff in the ULA power spectrum is also followed by a mild falloff, albeit at very small power.

Self-similar solutions for fuzzy dark matter

Fuzzy dark matter (FDM) models admit self-similar solutions which are very different from the standard cold dark matter (CDM) self-similar solutions and do not converge to the latter in the semiclassical limit. In contrast with the familiar CDM hierarchical collapse, they correspond to an inverse-hierarchy blowup. Constant-mass shells start in the nonlinear regime, at early times, with small radii and high densities, and expand to reach at late times the Hubble flow, up to small linear perturbations. Thus, larger masses become linear first. This blowup approximately follows the Hubble expansion, so that the central density contrast remains constant with time, although the width of the self-similar profile shrinks in comoving coordinates. As in a gravitational cooling process, matter is ejected from the central peaks through successive clumps. As in wave systems, the velocities of the geometrical structures and of the matter do not coincide, and matter slowly moves from one clump to the next, with intermittent velocity bursts at the transitions. These features are best observed using the density-velocity representation of the nonrelativistic scalar field, or the mass-shell trajectories, than with the Husimi phase-space distribution, where an analog of the Heisenberg uncertainty principle blurs the resolution in the position or velocity direction. These behaviors are due to the quantum pressure and the wavelike properties of the Schr\"odinger equation. Although the latter has been used as an alternative to $N$-body simulations for CDM, these self-similar solutions show that the semiclassical limit needs to be handled with care.

Quantum Tunneling of Fuzzy Dark Matter out of Satellite Galaxies

I show that the tidal gravitational potential of the Milky Way galaxy removes fuzzy dark matter from its satellite dwarf galaxies through quantum-mechanical tunneling. The existence of dark matter in satellites rules-out ultra-light axions as dark matter with a particle mass, m a < 2 × 10−21 eV. This limit exceeds the canonical mass range proposed as a solution to the small-scale challenges of the cold-dark-matter paradigm.

Solitons in the dark: First approach to non-linear structure formation with fuzzy dark matter

We present the results of a full cosmological simulation with the new codeSCALAR, where dark matter is in the form of fuzzy dark matter (FDM), described by a light scalar field with a mass ofmB = 2.5 × 10−22eV and evolving according to the Schrödinger-Poisson system of equations. In comoving units, the simulation volume is 2.5 h−1Mpc on a side, with a resolution of 20 h−1pc at the highest refinement level. While the resulting large-scale resolution prevents us from studying the general properties of the FDM structure formation, the extremely high small-scale resolution allows a detailed analysis of the formation and evolution of central solitonic cores, which are found to leave their imprints on dark matter density profiles, resulting in shallower central densities, and on rotation curves, producing an additional circular velocity peak at small radii from the centre. Despite the limitations on the large-scale resolution, we find that the suppression of structures due to the quantum nature of the scalar field reveals indications of a shallower halo mass function in the low-mass end compared to the case of a ΛCDM simulation, in which dark matter is expected to cluster at all mass scales even if it was evolved with the same initial conditions as used for FDM. Furthermore, we verify the scaling relations characterising the solution to the Schrödinger–Poisson system for both isolated and merging haloes, and we find that they are preserved by merging processes. We characterise each FDM halo in terms of the dimensionless quantity Ξ ∝ Ehalo/Mhalo3, and we show that the core mass is tightly linked to the halo mass by the core–halo mass relationMcore/Mhalo ∝ Ξ1/3. We also show that the core surface density of the simulated FDM haloes does not follow the scaling with the core radius, as observed for dwarf galaxies. This is a challenge for the FDM model as the sole explanation of core formation.

Could trapped quintessence account for the laser-detuning-dependent acceleration of cold atoms in varying-frequency time-of-flight experiments?

Using a trapped quintessence model, a series of time-of-flight (TOF) experiments with a different frequency of probe light were designed and performed. The varying-frequency TOF (VFTOF) experiments demonstrated that the fall acceleration of test atoms is dependent on the detuning of the probe light frequency with respect to the atomic transition frequency. In appropriately designed experiments, if the scalar field in the model accounts for the accelerated expansion of the Universe entirely, the field will result in an observable fifth force. Meanwhile, the trapped quintessence model still satisfies all experimental bounds on deviations from general relativity due to both the saturation effect and the short interaction range of the scalar field. The scalar saturates at a value corresponding to the cosmological constant when the microscopic nonrelativistic matter density is large enough. The interaction range of the scalar is inversely proportional to the square root of the microscopic nonrelativistic matter density. The interaction range has been estimated to be several $\mu \rm{m}$ in the current cosmic density. The Universe is assumed to be permeated with fuzzy dark matter, which means that the microscopic nonrelativistic matter density defined through the quantum wavefunctions of the ultralight particles can be used on the cosmic scale. By measuring the fall acceleration of the test atoms with the TOF method step-by-step in the detuning frequency domain of the probe light, we derived the dispersion curves of the measured acceleration versus the frequency detuning of the probe light. When the nonrelativistic matter density of the source increased due to the energy gained from the laser light, the test atoms were pulled to the center of the source, and vice versa.

Exploring delaying and heating effects on the 21-cm signature of fuzzy dark matter

In the fuzzy dark matter (FDM) model, dark matter is composed of ultra-light particles with a de Broglie wavelength of $\sim$kpc, above which it behaves like cold dark matter (CDM). Due to this, FDM suppresses the growth of structure on small scales, which delays the onset of the cosmic dawn (CD) and the subsequent epoch of reionization (EoR). This leaves potential signatures in the sky averaged 21-cm signal (global), as well as in the 21-cm fluctuations, which can be sought for with ongoing and future 21-cm global and intensity mapping experiments. To do so reliably, it is crucial to include effects such as the dark-matter/baryon relative velocity and Lyman-Werner star-formation feedback, which also act as delaying mechanisms, as well as CMB and \lya heating effects, which can significantly change the amplitude and timing of the signal, depending on the strength of X-ray heating sourced by the remnants of the first stars. Here we model the 21-cm signal in FDM cosmologies across CD and EoR using a modified version of the public code 21cmvFAST that accounts for all these additional effects, and is directly interfaced with the Boltzmann code CLASS so that degeneracies between cosmological and astrophysical parameters can be fully explored. We examine the prospects to distinguish between the CDM and FDM models and forecast joint astrophysical, cosmological and FDM parameter constraints achievable with intensity mapping experiments such as HERA and global signal experiments like EDGES. We find that HERA will be able to detect FDM particle masses up to $m_{\rm FDM}\! \sim \!10^{-19}\,{\rm eV}\!-\!10^{-18}\,{\rm eV}$, depending on foreground assumptions, despite the mitigating effect of the delaying and heating mechanisms included in the analysis.