Fuzzy Dark Matter Research Articles

The Effective Field Theory of Large-scale Structures of a Fuzzy Dark Matter Universe

Ultralight scalar fields and their noninteracting class, i.e., the so-called fuzzy dark matter (FDM), are dark matter candidates introduced to solve the small-scale problems of the standard cold dark matter. In this paper, we investigate whether the physics of FDM, particularly the quantum pressure that leads to the suppression of structure formation on small scales, could leave significant imprints on the large-scale statistics of matter fluctuations. For this purpose, we utilize the Effective Field Theory of Large Scale Structures (EFT of LSS), wherein small-scale physics is integrated and represented on large scales by only a set of free parameters. These parameters can be determined by fitting them into the cosmological simulations. By fitting the EFT predictions to the simulation data, we determine the value of the speed of sound as a quantitative measure of how UV physics affects large-scale perturbation. We use the Gadget-2 code to study the evolution of 5123 particles in a box with a side length 250 h −1 Mpc. We exploit the suppressed FDM initial power for the FDM universe and perform N-body simulation sufficient to produce accurate—enough for our purpose—results on large scales. In particular, we perform three FDM simulations with different masses and compare their sound speed with the standard cold dark matter (CDM) simulation. We found no difference between the FDM and CDM sound speeds beyond the confidence intervals. However, a consistently increasing trend can be seen in the sound speed for lower masses. This result suggests further investigations using higher-resolution simulations.

A weak lensing perspective on non-linear structure formation with fuzzy dark matter

ABSTRACT We investigate non-linear structure formation in the context of the fuzzy dark matter (FDM) model and compare it to the cold dark matter (CDM) model from a weak lensing perspective. Employing Eulerian perturbation theory (PT) up to fourth order, we calculate the tree-level matter trispectra and the one-loop matter spectra and bispectra from consistently chosen initial conditions. Furthermore, we conduct N-body simulations with CDM and FDM initial conditions to predict the non-linear matter power spectra. Subsequently, we derive the respective lensing spectra, bispectra, and trispectra for CDM and FDM within the framework of a Euclid-like weak lensing survey. In our analysis, we compute attainable cumulative signal-to-noise ratios and estimate χ2-functionals, aimed at distinguishing FDM from CDM at particle masses of m = 10−21 eV, m = 10−22 eV, and m = 10−23 eV. Our results indicate that PT predictions are insufficient for distinguishing between the CDM and FDM models within the context of our simulated weak lensing survey for the considered particle masses. Assuming that N-body simulations overestimate late-time small-scale power in the FDM model, future weak lensing surveys may provide the means to discriminate between FDM and CDM up to a mass of m = 10−23 eV. However, for stronger constraints on the FDM mass, observations of the local high-z universe may be more suitable.

Modelling post-reionization H i distributions in fuzzy dark matter cosmologies using conditional normalizing flows

ABSTRACT Upcoming 21-cm intensity mapping experiments like the Square Kilometer Array (SKA) hold significant potential to constrain the properties of dark matter. In this work, we model neutral hydrogen (H i) distributions using high-resolution hydrodynamical N-body simulations of both cold dark matter (CDM) and fuzzy dark matter (FDM) cosmologies in the post-reionization redshift range of z = 3.42−4.94. We show that the H i abundance decreases in FDM-like cosmologies. Extreme FDM models with m ∼ 10−22 eV are at odds with a range of measurements. Due to the increased halo bias, the H i bias increases, paralleled by the damped Lyman-α (DLA) bias which we infer from the cross-section of DLAs. The distribution of the latter in extreme FDM models has a high median at the low-mass end, which can be traced to the high column density of cosmic filaments. FDM models exhibit a very similar abundance of DLAs compared to CDM while sub-DLAs are already less abundant. We study the prospects of detecting the brightest H i peaks with SKA1-Low at z = 4.94, indicating moderate signal-to-noise ratios (SNRs) at angular resolution θA = 2 arcmin with a rapidly declining SNR for lower values of θA. After training the conditional normalizing flow network HIGlow on 2D H i maps, we interpolate its latent space of axion masses to predict the peak flux for a new, synthetic FDM cosmology, finding good agreement with expectations. This work thus underscores the potential of normalizing flows in capturing complex, non-linear structures within H i maps, offering a versatile tool for conditional sample generation and prediction tasks.

Generating fuzzy dark matter droplets

This research aims to explore the possibility of constructing black hole (BH) surrounded by fuzzy dark matter (DM) haloes, based on the Einasto density profile. Furthermore, the study offers the possibility of including DM as the matter component making up the BH and also presents a generalization of the non-commutative mini BH models. We describe how the coupling of the Einasto profile with an anisotropic stress–energy tensor gives rise to different BH solutions corresponding to each value of the Einasto index and the rescaled mass parameter. The assumption of de Sitter-type equation of state (EOS), i.e., ρ=−pr, offers the possibility of constructing BH solution or a fuzzy self-gravitational DM droplet based on the values of the mass parameter. However, in the case of a non-local EOS, the corresponding structure can be a self-gravitational fuzzy DM droplet with negative radial pressure. Finally, we consider the possibility of BHs originating from DM existing in galactic centers. Mainly, we examine whether such types of BHs could possibly serve as the central objects within galaxies.

Fuzzy dark matter dynamics and the quasi-particle hypothesis

ABSTRACT Dark matter may be composed of ultralight bosons whose de Broglie wavelength in galaxies is $\lambda \sim 1\, {\rm kpc}$. The standard model for this fuzzy dark matter (FDM) is a complex scalar field that obeys the Schrödinger–Poisson equations. The wavelike nature of FDM leads to fluctuations in the gravitational field that can pump energy into the stellar components of a galaxy. Heuristic arguments and theoretical analyses suggest that these fluctuations can be modelled by replacing FDM with a system of quasi-particles (QPs). We test this hypothesis by comparing self-consistent simulations of a Schrödinger field with those using a system of QPs in one spatial dimension. Simulations of pure FDM systems allow us to derive a phenomenological relation between the number of QPs that is required to model FDM with a given de Broglie wavelength. We also simulate systems of FDM and stars and find that the FDM pumps energy into the stars whether it is described by QPs or a Schrödinger field with the FDM adiabatically contracting and the stellar system adiabatically expanding. However, we find that QPs overestimate dynamical heating.

Nested solitons in two-field fuzzy dark matter

ABSTRACT Dark matter as scalar particles consisting of multiple species is well motivated in string theory where axion fields are ubiquitous. A two-field fuzzy dark matter (FDM) model features two species of ultralight axion particles with different masses, m1 ≠ m2, which is extended from the standard one-field model with $m_a \sim 10^{-22} \, {\rm eV}$. Here we perform numerical simulations to explore the properties of two-field FDM haloes. We find that the central soliton has a nested structure when m2 ≫ m1, which is distinguishable from the generic flat-core soliton in one-field haloes. However, the formation of this nested soliton is subject to many factors, including the density fraction and mass ratio of the two fields. Finally, we study non-linear structure formation in two-field cosmological simulations with self-consistent initial conditions and find that the small-scale structure in two-field cosmology is also distinct from the one-field model in terms of DM halo counts and soliton formation time.

Thesan-hr: galaxies in the Epoch of Reionization in warm dark matter, fuzzy dark matter, and interacting dark matter

ABSTRACT Using high-resolution cosmological radiation-hydrodynamic (RHD) simulations (thesan-hr), we explore the impact of alternative dark matter (altDM) models on galaxies during the Epoch of Reionization. The simulations adopt the IllustrisTNG galaxy formation model. We focus on altDM models that exhibit small-scale suppression of the matter power spectrum, namely warm dark matter (WDM), fuzzy dark matter (FDM), and interacting dark matter (IDM) with strong dark acoustic oscillations (sDAO). In altDM scenarios, both the halo mass functions and the ultraviolet luminosity functions at z ≳ 6 are suppressed at the low-mass/faint end, leading to delayed global star formation and reionization histories. However, strong non-linear effects enable altDM models to ‘catch up’ with cold dark matter (CDM) in terms of star formation and reionization. The specific star formation rates are enhanced in halos below the half-power mass in altDM models. This enhancement coincides with increased gas abundance, reduced gas depletion times, more compact galaxy sizes, and steeper metallicity gradients at the outskirts of the galaxies. These changes in galaxy properties can help disentangle altDM signatures from a range of astrophysical uncertainties. Meanwhile, it is the first time that altDM models have been studied in RHD simulations of galaxy formation. We uncover significant systematic uncertainties in reionization assumptions on the faint-end luminosity function. This underscores the necessity of accurately modeling the small-scale morphology of reionization in making predictions for the low-mass galaxy population. Upcoming James Webb Space Telescope imaging surveys of deep lensed fields hold potential for uncovering the faint low-mass galaxy population, which could provide constraints on altDM models.

Unified description of corpuscular and fuzzy bosonic dark matter

Unified description of corpuscular and fuzzy bosonic dark matter

Dark matter induced stellar oscillations

ABSTRACT It has been hypothesized that dark matter is comprised of ultra-light bosons whose collective phenomena can be described as a scalar field undergoing coherent oscillations. Examples include axion and fuzzy dark matter models. In this ultra-light dark matter (ULDM) scenario, the harmonic variation in the field’s energy–momentum tensor sources an oscillating component of the gravitational potential that we show can resonantly excite stellar oscillations. A mathematical framework for predicting the amplitude of these oscillations is developed, which reveals that ULDM predominantly excites p-modes of degree l = 1. An investigation of resonantly excited solar oscillations is presented, from which we conclude that dark matter induced oscillations of the Sun are likely undetectable. We discuss prospects for constraining ULDM using other stellar objects.

Structure, Kinematics, and Observability of the Large Magellanic Cloud’s Dynamical Friction Wake in Cold versus Fuzzy Dark Matter

The Large Magellanic Cloud (LMC) will induce a dynamical friction (DF) wake on infall to the Milky Way (MW). The MW’s stellar halo will respond to the gravity of the LMC and the dark matter (DM) wake, forming a stellar counterpart to the DM wake. This provides a novel opportunity to constrain the properties of the DM particle. We present a suite of high-resolution, windtunnel-style simulations of the LMC's DF wake that compare the structure, kinematics, and stellar tracer response of the DM wake in cold DM (CDM), with and without self-gravity, versus fuzzy DM (FDM) with m a = 10−23 eV. We conclude that the self-gravity of the DM wake cannot be ignored. Its inclusion raises the wake’s density by ∼10%, and holds the wake together over larger distances (∼50 kpc) than if self-gravity is ignored. The DM wake’s mass is comparable to the LMC’s infall mass, meaning the DM wake is a significant perturber to the dynamics of MW halo tracers. An FDM wake is more granular in structure and is ∼20% dynamically colder than a CDM wake, but with comparable density. The granularity of an FDM wake increases the stars’ kinematic response at the percent level compared to CDM, providing a possible avenue of distinguishing a CDM versus FDM wake. This underscores the need for kinematic measurements of stars in the stellar halo at distances of 70–100 kpc.

High-Quality Axions in a Class of Chiral U(1) Gauge Theories.

We show that there are many candidates for the quintessence and/or the QCD axions in a class of chiral U(1) gauge theories. Their qualities are high enough to serve as the dark energy and/or to solve the strong CP problem. Interestingly, the high quality of axion is guaranteed by the gauged U(1) and Z_{2N} symmetries and hence free from the nonperturbative quantum gravity corrections. Furthermore, our mechanism can be easily applied to the Fuzzy dark matter axion scenarios.

Towards super-resolution simulations of the fuzzy dark matter cosmological model

ABSTRACT AI super-resolution, combining deep learning and N-body simulations, has been shown to successfully reproduce the large-scale structure and halo abundances in the Lambda cold dark matter cosmological model. Here, we extend its use to models with a different dark matter content, in this case fuzzy dark matter (FDM), in the approximation that the difference is encoded in the initial power spectrum. We focus on redshift z = 2, with simulations that model smaller scales and lower masses, the latter by two orders of magnitude, than has been done in previous AI super-resolution work. We find that the super-resolution technique can reproduce the power spectrum and halo mass function to within a few per cent of full high-resolution calculations. We also find that halo artefacts, caused by spurious numerical fragmentation of filaments, are equally present in the super-resolution outputs. Although we have not trained the super-resolution algorithm using full quantum pressure FDM simulations, the fact that it performs well at the relevant length and mass scales means that it has promise as a technique that could avoid the very high computational cost of the latter, in some contexts. We conclude that AI super-resolution can become a useful tool to extend the range of dark matter models covered in mock catalogues.

Confronting fuzzy dark matter with the rotation curves of nearby dwarf irregular galaxies

Aims. In this paper, we carry out a phenomenological investigation of the viability of fuzzy dark matter, which is composed of coherent waves of non-interacting ultralight axions with a mass of ma ≈ 10−22 eV. We did so by confronting the predictions of the model, in particular, the formation of a solitonic core at the center of dark matter halos, with a homogeneous and robust sample of high-resolution rotation curves from the LITTLE THINGS in 3D catalog. This comprises a collection of isolated, dark matter-dominated dwarf-irregular galaxies that provides an optimal benchmark for cosmological studies. Our aim is to find evidence of fuzzy dark matter in the observations; alternatively, we seek to set exclusion ranges for its mass. Methods. We used a statistical framework based on a χ2 analysis of the rotation curves of the LITTLE THINGS in 3D catalog using a fuzzy dark matter profile as the theoretical model. This allows us to extract relevant parameters such as the axion mass and mass of the solitonic core, as well as the mass of the dark matter halo and its concentration parameter. We fit the data using current Markov chain Monte Carlo techniques with a rather loose set of priors, except for the implementation of a core-halo relation predicted by simulations. The results of the fits were then used to perform various diagnostics on the predictions of the model. Results. Fuzzy dark matter provides an excellent fit to the rotation curves of the LITTLE THINGS in 3D catalog, with axion masses determined from different galaxies clustering around ma ≈ 2 × 10−23 eV. However, we find two major problems from our analysis. First, the data follow scaling relations of the properties of the core, which are not consistent with the predictions of the soliton. This problem is particularly acute in the core radius-mass relation with a tension that (at face value) has a significance of ≳5σ. The second problem is related to the strong suppression of the linear power spectrum that is predicted by fuzzy dark matter for the axion mass preferred by the data. This can be constrained very conservatively by the galaxy counts in our sample, which leads to a tension that exceeds 5σ. We estimate the effects of baryons in our analysis and discuss whether they could alleviate the tensions of the model with observations.

Cosmic web dissection in fuzzy dark matter cosmologies

ABSTRACT On large cosmological scales, anisotropic gravitational collapse is manifest in the dark cosmic web. Its statistical properties are little known for alternative dark matter (DM) models such as fuzzy dark matter (FDM). In this work, we assess for the first time the relative importance of cosmic nodes, filaments, walls, and voids in a cosmology with primordial small-scale suppression of power. We post-process N-body simulations of FDM-like cosmologies with varying axion mass m at redshifts z ∼ 1.0−5.6 using the NEXUS+ Multiscale Morphology Filter technique at smoothing scale Δx = 0.04 h−1 Mpc. The formation of wall and void halos is more suppressed than naively expected from the half-mode mass M1/2. Also, we quantify the mass- and volume-filling fractions of cosmic environments and find that 2D cosmic sheets host a larger share of the matter content of the Universe as m is reduced, with an ∼8−12 per cent increase for the m = 7 × 10−22 eV model compared to cold dark matter (CDM). We show that in FDM-like cosmologies, filaments, walls, and voids are cleaner and more pronounced structures than in CDM, revealed by a strong mid-range peak in the conditioned overdensity PDFs P(δ). At high redshift, low-density regions are more suppressed than high-density regions. Furthermore, skewness estimates S3 of the total overdensity PDF in FDM-like cosmologies are consistently higher than in CDM, especially at high redshift z ∼ 5.6 where the m = 10−22 eV model differs from CDM by ∼6σ. Accordingly, we advocate for the usage of P(δ) as a testbed for constraining FDM and other alternative DM models.

The halo mass function and filaments in full cosmological simulations with fuzzy dark matter

ABSTRACT Fuzzy dark matter (FDM) is a dark matter candidate consisting of ultralight scalar particles with masses around $10^{-22}\, \mathrm{eV}/c^2$, a regime where cold bosonic matter behaves as a collective wave rather than individual particles. Although constraints on FDM are accumulating in many different contexts, very few have been verified by self-consistent numerical simulations. We present new large numerical simulations of cosmic structure formation with FDM, solving the full Schrödinger–Poisson (SP) equations using the AxiREPO code, which implements a pseudo-spectral numerical method. Combined with our previous simulations, they allow us to draw a four-way comparison of matter clustering, contrasting results (such as power spectra) for each combination of initial conditions (ICs; FDM versus cold dark matter, CDM) and dynamics (SP versus N-body). By disentangling the impact of ICs and non-linear dynamics in this manner, we can gauge the validity of approximate methods used in previous works, such as ordinary N-body simulations with an FDM initial power spectrum. Due to the comparatively large volume achieved in our FDM simulations, we are able to measure the FDM halo mass function from full wave simulations for the first time, and compare to previous results obtained using analytic or approximate approaches. We also investigate the density profiles of these filaments and compare to their ΛCDM counterparts.

Self-similar solutions for fuzzy dark matter

Self-similar solutions for fuzzy dark matter are very different from their counterparts in the standard cold dark matter model. In contrast to the familiar hierarchical collapse of the current model for structure formation, they correspond to an inverse hierarchical blow-up. This fact highlights the gravitational cooling process, which in the absence of dissipation, allows the system to eject excess energy through the intermittent expulsion of clumps of matter. These surprising behaviours are due to the wave properties of the Schrödinger equation and to the quantum pressure. These features are printed in the Eulerian density-velocity representation of the nonrelativistic scalar field, or in the Lagrangian representation in the mass-shell trajectories.

Fuzzy dark matter in relativistic stars

ABSTRACT Fuzzy dark matter (FDM), a practical alternative to cold dark matter, can exist in compact stars. Here, applying the FDM equation of state (EoS) constrained by cosmic microwave background and large-scale structure data, we calculate the structure of relativistic stars in the presence of FDM. For this aim, the EoS for the visible matter in neutron stars, quark stars, and hybrid stars from the observational data are employed. A piecewise polytropic EoS constrained by the observational data of GW170817 and the data of six low-mass X-ray binaries with thermonuclear burst or the symmetry energy of the nuclear interaction describes the neutron star matter. For quark star matter, we apply the EoSs within the Bayesian statistical approach using the mass and radius measurements of PSR J0030+0451 from NICER. Employing the two-fluid formalism, we study the structure of FDM admixed relativistic stars.

Microlensing of gravitational waves by dark matter structures

Gravitational lensing of gravitational waves provides a potential new probe of dark matter structures. In this work, we consider the microlensing effect on gravitational wave signals from black hole binaries induced by low-mass dark matter halos that do not retain enough baryonic matter to hold stars. We clarify systematically when this microlensing effect is relevant and study in detail its detectability by future gravitational wave observatories. We consider lensing by cold dark matter halos and by solitonic cores that reside in fuzzy dark matter halos. Our results show that although the effect can be detectable at relatively large impact parameters, the probability of detecting such lensed events is low. In particular, we find that the expected number of events lensed by cold dark matter halos is 𝒪(0.01) per year for BBO and the expected number of events lensed by solitonic cores inside fuzzy dark matter halos is 𝒪(0.01) per year for ET. In the case that a significant fraction of dark matter consists of 𝒪(100 M ⊙) objects that are relatively compact, R < 𝒪(0.1 pc), we show that the expected number of lensed events per year for ET can be very large, 𝒪(1000).

Effect of boundary conditions on structure formation in fuzzy dark matter

We illustrate the effect of boundary conditions on the evolution of structure in fuzzy dark matter. Scenarios explored include the evolution of single, ground-state equilibrium solutions of the Schr\"odinger-Poisson system, relaxation of a Gaussian density fluctuation, mergers of two equilibrium configurations, and the random merger of many solitons. For comparison, each scenario is evolved twice, with isolation vs periodic boundary conditions, the two commonly used to simulate isolated systems and structure formation, respectively. Replacing isolation boundary conditions (implemented by an absorbing sponge at large radius) by periodic boundary conditions changes the domain topology and dynamics of each scenario by affecting the outcome of gravitational cooling. With periodic boundary conditions, the initial ground-state equilibrium solution and Gaussian fluctuation each evolve toward the single equilibrium solitonic core of the isolated case, but surrounded by an envelope, or tail, in which additional mass is distributed nearly uniformly, unlike the isolated versions. The case of head-on, binary merger introduces additional effects caused by the pull on the system due to the infinite network of periodic images along each axis of the domain. Adding angular momentum to this binary merger results in a tail with polynomial profile when using a periodic domain. Finally, the 3D merger of many, randomly placed solitonic cores of different mass makes a solitonic core surrounded by a tail with power-law-like profile, for periodic boundary conditions, while producing a core with a much sharper falloff in the isolated case. This suggests the conclusion of earlier work, that the ground-state equilibrium solution is an attractor for the asymptotic state, is true even in 3D and for more general circumstances than previously considered, but only if gravitational cooling is able to carry mass and energy off to infinity, which isolation boundary conditions allow, but periodic ones do not.

A lensed radio jet at milli-arcsecond resolution – II. Constraints on fuzzy dark matter from an extended gravitational arc

ABSTRACT Using a single gravitational lens system observed at ≲ 5 mas resolution with very long baseline interferometry, we place a lower bound on the mass of the fuzzy dark matter (FDM) particle, ruling out mχ ≤ 4.4 × 10−21 eV with a 20:1 posterior odds ratio relative to a smooth lens model. We generalize our result to non-scalar and multiple-field models, such as vector FDM, with mχ,vec &amp;gt; 1.4 × 10−21 eV. Due to the extended source structure and high angular resolution of the observation, our analysis is directly sensitive to the presence of granule structures in the main dark matter halo of the lens, which is the most generic prediction of FDM theories. A model based on well-understood physics of ultra-light dark matter fields in a gravitational potential well makes our result robust to a wide range of assumed dark matter fractions and velocity dispersions in the lens galaxy. Our result is competitive with other lower bounds on mχ from past analyses, which rely on intermediate modelling of structure formation and/or baryonic effects. Higher resolution observations taken at 10–100 GHz could improve our constraints by up to two orders of magnitude in the future.