Ultralight Bosons Research Articles

Probing the existence of ultralight bosons with a single gravitational-wave measurement

Light bosons, proposed as a possible solution to various problems in fundamental physics and cosmology, include a broad class of candidates for beyond the Standard Model physics, such as dilatons and moduli, wave dark matter and axion-like particles. If light bosons exist in nature, they will spontaneously form "clouds" by extracting rotational energy from rotating massive black holes through superradiance, a classical wave amplification process that has been studied for decades. The superradiant growth of the cloud sets the geometry of the final black hole, and the black hole geometry determines the shape of the cloud. Hence, both the black hole geometry and the cloud encode information about the light boson. For this reason, measurements of the gravitational field of the black hole/cloud system (as encoded in gravitational waves) are over-determined. We show that a single gravitational wave measurement can be used to verify the existence of light bosons by model selection, rule out alternative explanations for the signal, and measure the boson mass. Such measurements can be done generically for bosons in the mass range $[10^{-16.5},10^{-14}]$ eV using LISA observations of extreme mass-ratio inspirals.

Spherical collapse of fuzzy dark matter

It has been postulated that Fuzzy Dark Matter (FDM) could be a viable alternative to Cold Dark Matter (CDM). FDM is comprised of ultralight bosons which exist as a Bose-Einstein condensate. Due to the very low mass of FDM, the de Broglie wavelength of these bosons are of the order of kpc and the quantum effects manifest at those scales. Hence, unlike CDM, FDM experiences quantum pressure along with gravitational attraction. In this work, we investigate the gravitational collapse of a spherically symmetric FDM overdensity. We assume a power law density profile for an overdense region of FDM and derive an expression for the temporal evolution of a spherical shell in the non-interacting limit and use it to derive an expression for average overdensity contained in the spherical shell in an Einstein--de Sitter universe. Further, we numerically extend the analysis to the case of interacting bosons. Finally, we discuss the virialization of such an overdense region of non-interacting FDM and derive an expression for overdensity in the linear and the full theory. We compare our results with those obtained in the case of CDM and conclude with a discussion of the results.

Heating of Milky Way disc stars by dark matter fluctuations in cold dark matter and fuzzy dark matter paradigms

ABSTRACT Although highly successful on cosmological scales, cold dark matter (CDM) models predict unobserved overdense ‘cusps’ in dwarf galaxies and overestimate their formation rate. We consider an ultralight axion-like scalar boson which promises to reduce these observational discrepancies at galactic scales. The model, known as fuzzy dark matter (FDM), avoids cusps, suppresses small-scale power, and delays galaxy formation via macroscopic quantum pressure. We compare the substructure and density fluctuations of galactic dark matter haloes comprised of ultralight axions to conventional CDM results. Besides self-gravitating subhaloes, FDM includes non-virialized overdense wavelets formed by quantum interference patterns, which are an efficient source of heating to galactic discs. We find that, in the solar neighbourhood, wavelet heating is sufficient to give the oldest disc stars a velocity dispersion of ${\sim } {30}{\, \mathrm{km\, s}^{-1}}$ within a Hubble time if energy is not lost from the disc, the velocity dispersion increasing with stellar age as σD ∝ t0.4 in agreement with observations. Furthermore, we calculate the radius-dependent velocity dispersion and corresponding scaleheight caused by the heating of this dynamical substructure in both CDM and FDM with the determination that these effects will produce a flaring that terminates the Milky Way disc at $15\!-\!20{\, \mathrm{kpc}}$. Although the source of thickened discs is not known, the heating due to perturbations caused by dark substructure cannot exceed the total disc velocity dispersion. Therefore, this work provides a lower bound on the FDM particle mass of ma > 0.6 × 10−22 eV. Furthermore, FDM wavelets with this particle mass should be considered a viable mechanism for producing the observed disc thickening with time.

Probing ultralight bosons with binary black holes

We study the gravitational-wave (GW) signatures of clouds of ultralight bosons around black holes (BHs) in binary inspirals. These clouds, which are formed via superradiance instabilities for rapidly rotating BHs, produce distinct effects in the population of BH masses and spins, and a continuous monochromatic GW signal. We show that the presence of a binary companion greatly enriches the dynamical evolution of the system, most remarkably through the existence of resonant transitions between the growing and decaying modes of the cloud (analogous to Rabi oscillations in atomic physics). These resonances have rich phenomenological implications for current and future GW detectors. Notably, the amplitude of the GW signal from the clouds may be reduced, and in many cases terminated, much before the binary merger. The presence of a boson cloud can also be revealed in the GW signal from the binary through the imprint of finite-size effects, such as spin-induced multipole moments and tidal Love numbers. The time dependence of the cloud's energy density during the resonance leads to a sharp feature, or at least attenuation, in the contribution from the finite-size terms to the waveforms. The observation of these effects would constrain the properties of putative ultralight bosons through precision GW data, offering new probes of physics beyond the Standard Model.

Semicoherent analysis method to search for continuous gravitational waves emitted by ultralight boson clouds around spinning black holes

As a consequence of superradiant instability induced in Kerr black holes, ultra-light boson clouds can be a source of persistent gravitational waves, potentially detectable by current and future gravitational-wave detectors. These signals have been predicted to be nearly monochromatic, with a small steady frequency increase (spin-up), but given the several assumptions and simplifications done at theoretical level, it is wise to consider, from the data analysis point of view, a broader class of gravitational signals in which the phase (or the frequency) slightly wander in time. Also other types of sources, e.g. neutron stars in which a torque balance equilibrium exists between matter accretion and emission of persistent gravitational waves, would fit in this category. In this paper we present a robust and computationally cheap analysis pipeline devoted to the search of such kind of signals. We provide a full characterization of the method, through both a theoretical sensitivity estimation and through the analysis of syntethic data in which simulated signals have been injected. The search setup for both all-sky searches and higher sensitivity directed searches is discussed.

Parkes Pulsar Timing Array constraints on ultralight scalar-field dark matter

It is widely accepted that dark matter contributes about a quarter of the critical mass-energy density in our Universe. The nature of dark matter is currently unknown, with the mass of possible constituents spanning nearly one hundred orders of magnitude. The ultralight scalar field dark matter, consisting of extremely light bosons with $m \sim 10^{-22}$ eV and often called "fuzzy" dark matter, provides intriguing solutions to some challenges at sub-Galactic scales for the standard cold dark matter model. As shown by Khmelnitsky and Rubakov, such a scalar field in the Galaxy would produce an oscillating gravitational potential with nanohertz frequencies, resulting in periodic variations in the times of arrival of radio pulses from pulsars. The Parkes Pulsar Timing Array (PPTA) has been monitoring 20 millisecond pulsars at two to three weeks intervals for more than a decade. In addition to the detection of nanohertz gravitational waves, PPTA offers the opportunity for direct searches for fuzzy dark matter in an astrophysically feasible range of masses. We analyze the latest PPTA data set which includes timing observations for 26 pulsars made between 2004 and 2016. We perform a search in this data set for evidence of ultralight dark matter in the Galaxy using Bayesian and Frequentist methods. No statistically significant detection has been made. We therefore place upper limits on the local dark matter density. Our limits, improving on previous searches by a factor of two to five, constrain the dark matter density of ultralight bosons with $m \leq 10^{-23}$ eV to be below $6\,\text{GeV}\,\text{cm}^{-3}$ with 95\% confidence in the Earth neighborhood. Finally, we discuss the prospect of probing the astrophysically favored mass range $m \gtrsim 10^{-22}$ eV with next-generation pulsar timing facilities.

Jeans-type instability of a complex self-interacting scalar field in general relativity

We study the gravitational instability of a general relativistic complex scalar field with a quartic self-interaction in an infinite homogeneous static background. This quantum relativistic Jeans problem provides a simplified framework to study the formation of the large-scale structures of the Universe in the case where dark matter is made of a scalar field. The scalar field may represent the wave function of a relativistic self-gravitating Bose-Einstein condensate. Exact analytical expressions for the dispersion relation and Jeans length $\lambda_J$ are obtained from a hydrodynamical representation of the Klein-Gordon-Einstein equations. When relativistic effects are fully accounted for, we find that the perturbations are stabilized at very large scales of the order of the Hubble length $\lambda_H$. Numerical applications are made for ultralight bosons without self-interaction (fuzzy dark matter), for bosons with a repulsive self-interaction, and for bosons with an attractive self-interaction (QCD axions and ultralight axions). We show that the Jeans instability is inhibited in the ultrarelativistic regime (early Universe and radiationlike era) because the Jeans length is of the order of the Hubble length ($\lambda_J\sim\lambda_H$), except when the self-interaction of the bosons is attractive. By contrast, structure formation can take place in the nonrelativistic regime (matterlike era) for $\lambda_J\le \lambda\le \lambda_H$. Since the scalar field has a nonzero Jeans length due to its quantum nature (Heisenberg uncertainty principle or quantum pressure due to the self-interaction of the bosons), it appears that the wave properties of the scalar field can stabilize gravitational collapse at small scales, providing halo cores and suppressing small-scale linear power. This may solve the CDM crisis such as the cusp problem and the missing satellite problem.

Bose-Einstein condensate & degenerate Fermi cored dark matter halos

There has been considerable interest in the last several years in support of the idea that galaxies and clusters could have highly condensed cores of dark matter (DM) within their central regions. In particular, it has been suggested that dark matter could form Bose-Einstein condensates (BECs) or degenerate Fermi cores. We examine these possibilities under the assumption that the core consists of highly condensed DM (either bosons or fermions) that is embedded in a diffuse envelope (e.g., isothermal sphere). The novelty of our approach is that we invoke composite polytropes to model spherical collisionless structures in a way that is physically intuitive and can be generalized to include other equations of state (EOSs). Our model is very amenable to the analysis of BEC cores (composed of ultra-light bosons) that have been proposed to resolve small-scale CDM anomalies. We show that the analysis can readily be applied to bosons with or without small repulsive self-interactions. With respect to degenerate Fermi cores, we confirm that fermionic particle masses between 1—1000 keV are not excluded by the observations. Finally, we note that this approach can be extended to include a wide range of EOSs in addition to multi-component collisionless systems.

Hidden-sector Spectroscopy with Gravitational Waves from Binary Neutron Stars

Abstract We show that neutron star (NS) binaries can be ideal laboratories to probe hidden sectors with a long-range force. In particular, it is possible for gravitational wave (GW) detectors such as LIGO and Virgo to resolve the correction of waveforms from ultralight dark gauge bosons coupled to NSs. We observe that the interaction of the hidden sector affects both the GW frequency and amplitude in a way that cannot be fitted by pure gravity.

Can INO be sensitive to flavor-dependent long-range forces?

Flavor-dependent long-range leptonic forces mediated by the ultra-light and neutral bosons associated with gauged Le − Lμ or Le − Lτ symmetry constitute a minimal extension of the Standard Model. In presence of these new anomaly free abelian symmetries, the SM remains invariant and renormalizable, and can lead to interesting phenomenological consequences. For an example, the electrons inside the Sun can generate a flavor-dependent long-range potential at the Earth surface, which can enhance νμ and {overline{nu}}_{mu } survival probabilities over a wide range of energies and baselines in atmospheric neutrino experiments. In this paper, we explore in detail the possible impacts of these long-range flavor-diagonal neutral current interactions due to Le − Lμ and Le − Lτ symmetries (one at-a-time) in the context of proposed 50 kt magnetized ICAL detector at INO. Combining the information on muon momentum and hadron energy on an event-by-event basis, ICAL will be sensitive to long-range forces at 90% (3σ) C.L. with 500 kt·yr exposure if the effective gauge coupling αeμ/eτ> 1.2 × 10−53 (1.75 × 10−53). The sensitivity of ICAL towards αeμ (αeτ) is ∼ 46 (53) times better than the existing bound from the Super-Kamiokande experiment at 90% C.L., and at 3σ, the sensitivity of ICAL is comparable to the bounds obtained from the combined solar and KamLAND data.

On the possibility that ultra-light boson haloes host and form supermassive black holes

Several observations suggest the existence of super-massive black holes (SMBH) at the centers of giant galaxies. However the mechanism under which these objects form remains non completely understood. In this work we review an alternative mechanism of formation of galactic SMBHs. This is, the collapse of ultra-light scalar field configurations playing the role of dark matter halos. Several works have studied this scenario and investigated its plausibility. The theory of collapse of scalar field configurations into compact objects has been extensively studied regarding to boson stars, in this work we extrapolate such results for models of galactic halos hosting central SMBHs. We construct the simplest setup of an ultra-light scalar field configuration laying in a Schwarzschild space-time for modeling a galactic system with a SMBH in the quasi-static limit. This model is applicable to systems either out of their accretion-phase at late times or either for those undergoing into a very slow accretion-phase, such as some early-type giant elliptic galaxies and bulges. On the other hand, very recent direct observation of Sagittarius A by the Event Horizon Telescope will open an era of explorations of the deep-inner galactic region of the Milky Way that will enable us to test and distinguish various dark matter models. Thus we use our model to give a very first step towards that direction. We derive the stellar kinematics induced by this sort dark matter to obtain information of the black hole's influence into the observable features of the velocity field of visible matter deep inside the galaxy. Thus we compute the radial velocity, acceleration and velocity dispersion densities for some realistic cases.

Constraining the mass of dark photons and axion-like particles through black-hole superradiance

Ultralight bosons and axion-like particles appear naturally in different scenarios and could solve some long-standing puzzles. Their detection is challenging, and all direct methods hinge on unknown couplings to the Standard Model of particle physics. However, the universal coupling to gravity provides model-independent signatures for these fields. We explore here the superradiant instability of spinning black holes triggered in the presence of such fields. The instability taps angular momentum from and limits the maximum spin of astrophysical black holes. We compute, for the first time, the spectrum of the most unstable modes of a massive vector (Proca) field for generic black-hole spin and Proca mass. The observed stability of the inner disk of stellar-mass black holes can be used to derive direct constraints on the mass of dark photons in the mass range 10−13 eV≲ mV ≲ 3× 10−12 eV. By including also higher azimuthal modes, similar constraints apply to axion-like particles in the mass range 6×10−13 eV≲ mALP ≲ 10−11 eV. Likewise, mass and spin distributions of supermassive BHs—as measured through continuum fitting, Kα iron line, or with the future space-based gravitational-wave detector LISA – imply indirect bounds in the mass range approximately 10−19 eV≲ mV, mALP ≲ 10−13 eV, for both axion-like particles and dark photons. Overall, superradiance allows to explore a region of approximately 8 orders of magnitude in the mass of ultralight bosons.

A Model of Dark Matter and Dark Energy Based on Relativizing Newton’s Physics

The nature and properties of dark matter and dark energy in the universe are among the outstanding open issues of modern cosmology. Despite extensive theoretical and empirical efforts, the question “what is dark matter made of?” has not been answered satisfactorily. Candidates proposed to identify particle dark matter span over ninety orders of magnitude in mass, from ultra-light bosons, to massive black holes. Dark energy is a greater enigma. It is believed to be some kind of negative vacuum energy, responsible for driving galaxies apart in accelerated motion. In this article we take a relativistic approach in theorizing about dark matter and dark energy. Our approach is based on our recently proposed Information Relativity theory. Rather than theorizing about the identities of particle dark matter candidates, we investigate the relativistic effects on large scale celestial structures at their recession from an observer on Earth. We analyze a simplified model of the universe, in which large scale celestial bodies, like galaxies and galaxy clusters, are non-charged compact bodies that recede rectilinearly along the line-of-sight of an observer on Earth. We neglect contributions to dark matter caused by the rotation of celestial structures (e.g., the rotation of galaxies) and of their constituents (e.g., rotations of stars inside galaxies). We define the mass of dark matter as the complimentary portion of the derived relativistic mass, such that at any given recession velocity the sum of the two is equal to the Newtonian mass. The emerging picture from our analysis could be summarized as follows: 1) At any given redshift, the dark matter of a receding body exists in duality to its observable matter. 2) The dynamical interaction between the dark and the observed matter is determined by the body’s recession velocity (or redshift). 3) The observable matter mass density decreases with its recession velocity, with matter transforming to dark matter. 4) For redshifts z 0.5 the universe is dominated by dark matter. 5) Consistent with observational data, at redshift z = 0.5, the densities of matter and dark matter in the universe are predicted to be equal. 6) At redshift equaling the Golden Ratio (z ≈ 1.618), baryonic matter undergoes a quantum phase transition. The universe at higher redshifts is comprised of a dominant dark matter alongside with quantum matter. 7) Contrary to the current conjecture that dark energy is a negative vacuum energy that might interact with dark matter, comparisons of our theoretical results with observational results of ΛCDM cosmologies, and with observations of the relative densities of matter and dark energy at redshift z ≈ 0.55, allow us to conclude that dark energy is the energy carried by dark matter. 8) Application of the model to the case of rotating bodies, which will be discussed in detail in a subsequent paper, raises the intriguing possibility that the gravitational force between two bodies of mass is mediated by the entanglement of their dark matter components.

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.

Gravitational wave searches for ultralight bosons with LIGO and LISA

Ultralight bosons can induce superradiant instabilities in spinning black holes, tapping their rotational energy to trigger the growth of a bosonic condensate. Possible observational imprints of these boson clouds include (i) direct detection of the nearly monochromatic (resolvable or stochastic) gravitational waves emitted by the condensate, and (ii) statistically significant evidence for the formation of "holes" at large spins in the spin versus mass plane (sometimes also referred to as "Regge plane") of astrophysical black holes. In this work, we focus on the prospects of LISA and LIGO detecting or constraining scalars with mass in the range $m_s\in [10^{-19},\,10^{-15}]$ eV and $m_s\in [10^{-14},\,10^{-11}]$ eV, respectively. Using astrophysical models of black-hole populations calibrated to observations and black-hole perturbation theory calculations of the gravitational emission, we find that, in optimistic scenarios, LIGO could observe a stochastic background of gravitational radiation in the range $m_s\in [2\times 10^{-13}, 10^{-12}]$ eV, and up to $10^4$ resolvable events in a $4$-year search if $m_s\sim 3\times 10^{-13}\,{\rm eV}$. LISA could observe a stochastic background for boson masses in the range $m_s\in [5\times 10^{-19}, 5\times 10^{-16}]$, and up to $\sim 10^3$ resolvable events in a $4$-year search if $m_s\sim 10^{-17}\,{\rm eV}$. LISA could further measure spins for black-hole binaries with component masses in the range $[10^3, 10^7]~M_\odot$, which is not probed by traditional spin-measurement techniques. A statistical analysis of the spin distribution of these binaries could either rule out scalar fields in the mass range $\sim [4 \times 10^{-18}, 10^{-14}]$ eV, or measure $m_s$ with ten percent accuracy if light scalars in the mass range $\sim [10^{-17}, 10^{-13}]$ eV exist.

Stochastic and Resolvable Gravitational Waves from Ultralight Bosons.

Ultralight scalar fields around spinning black holes can trigger superradiant instabilities, forming a long-lived bosonic condensate outside the horizon. We use numerical solutions of the perturbed field equations and astrophysical models of massive and stellar-mass black hole populations to compute, for the first time, the stochastic gravitational-wave background from these sources. In optimistic scenarios the background is observable by Advanced LIGO and LISA for field masses m_{s} in the range ∼[2×10^{-13},10^{-12}] and ∼5×[10^{-19},10^{-16}] eV, respectively, and it can affect the detectability of resolvable sources. Our estimates suggest that an analysis of the stochastic background limits from LIGO O1 might already be used to marginally exclude axions with mass ∼10^{-12.5} eV. Semicoherent searches with Advanced LIGO (LISA) should detect ∼15(5) to 200(40) resolvable sources for scalar field masses 3×10^{-13} (10^{-17}) eV. LISA measurements of massive BH spins could either rule out bosons in the range ∼[10^{-18},2×10^{-13}] eV, or measure m_{s} with 10% accuracy in the range ∼[10^{-17},10^{-13}] eV.

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.

Superradiant instability of massive vector fields around spinning black holes in the relativistic regime

We study the superradiant instability of massive vector fields, i.e. Proca fields, around spinning black holes in the test field limit. This is motivated by the possibility that observations of astrophysical black holes can probe the existence of ultralight bosons subject to this mechanism. By making use of time-domain simulations, we characterize the growth rate, frequency, spatial distribution, and other properties of the unstable modes, including in the regime where the black hole is rapidly spinning and the Compton wavelength of the Proca field is comparable to the black hole radius. We find that relativistic effects in this regime increase the range of Proca masses that are unstable, as well as the maximum instability rate. We also study the gravitational waves that can be sourced by such an instability, finding that they can be significantly stronger than in the massive scalar field case.

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.

Cosmological evolution of a complex scalar field with repulsive or attractive self-interaction

We study the cosmological evolution of a complex scalar field with a self-interaction potential $V(|\varphi|^2)$, possibly describing self-gravitating Bose-Einstein condensates, using a fully general relativistic treatment. We generalize the hydrodynamic representation of the Klein-Gordon-Einstein equations in the weak field approximation developed in our previous paper. We establish the general equations governing the evolution of a spatially homogeneous complex scalar field in an expanding background. We show how they can be simplified in the fast oscillation regime and derive the equation of state of the scalar field in parametric form for an arbitrary potential. We explicitly consider the case of a quartic potential with repulsive or attractive self-interaction and determine the phase diagram of the scalar field. We show that the transition between the weakly self-interacting regime and the strongly self-interacting regime depends on how the scattering length of the bosons compares with their effective Schwarzschild radius. We also constrain the parameters of the scalar field from astrophysical and cosmological observations. Numerical applications are made for ultralight bosons without self-interaction (fuzzy dark matter), for bosons with repulsive self-interaction, and for bosons with attractive self-interaction (QCD axions and ultralight axions).