Bose-Einstein Condensate Dark Matter Research Articles

Extended Bose–Einstein condensate dark matter in f(Q) gravity

Extended Bose–Einstein condensate dark matter in f(Q) gravity

Temporal evolution of cosmological density perturbations of the Bose–Einstein condensate dark matter

Dark matter is assumed to be composed of scalar boson particles that form Bose–Einstein condensate during the cosmic evolution of the Universe when the temperature of the dark matter is below the critical temperature Tcr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{cr}$$\\end{document}. At around a redshift z∼1200\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z\\sim 1200$$\\end{document}, the normal dark matter converted to Bose–Einstein condensate dark matter through a first-order phase transition and continued to complete the condensation process for nearly 106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^6$$\\end{document} years, until then, both phases coexist. In this manuscript, considering Bose–Einstein condensate dark matter as a Gross–Pitaevskii–Poisson system, we study the time evolution of density contrast of Bose–Einstein condensate dark matter using cosmological linear perturbation theory following previous works on the subject. The evolution equation contains quantum pressure due to Heisenberg’s uncertainty principle and self-interaction pressure terms. We solve the temporal density contrast equation of Bose–Einstein condensate dark matter analytically for both the Thomas-Fermi limit and the non-interacting case where the expansion rule follows similarly to that of the Einstein–de Sitter Universe. In addition, we also numerically analyze the temporal nature of the evolution of density contrast of Bose–Einstein condensate dark matter for the complete equation without applying any approximation. We find that the Bose–Einstein condensate model of dark matter could modify the temporal nature of density contrast evolution due to the presence of self-interaction and quantum pressure terms, which shows significant differences with respect to the conventional standard cold dark matter, and successfully solves the small-scale problems in the context of cosmological structure formation.

Maximum mass of relativistic self-gravitating Bose-Einstein condensates with repulsive or attractive |φ|4 self-interaction

We derive an approximate analytical expression of the maximum mass of relativistic self-gravitating Bose-Einstein condensates with repulsive or attractive $|\ensuremath{\varphi}{|}^{4}$ self-interaction. This expression interpolates between the general relativistic maximum mass of noninteracting bosons stars, the general relativistic maximum mass of bosons stars with a repulsive self-interaction in the Thomas-Fermi limit, and the Newtonian maximum mass of dilute axion stars with an attractive self-interaction [P. H. Chavanis, Phys. Rev. D 84, 043531 (2011)]. We obtain the general structure of our formula from simple considerations and determine the numerical coefficients in order to recover the exact asymptotic expressions of the maximum mass in particular limits. As a result, our formula should provide a relevant approximation of the maximum mass of relativistic boson stars for any value (positive and negative) of the self-interaction parameter. We discuss the evolution of the system above the maximum mass and consider application of our results to dark matter halos and inflaton clusters. We also make a short review of boson stars and Bose-Einstein condensate dark matter halos and point out analogies with models of extended elementary particles.

Prospects of probing dark matter condensates with gravitational waves

The Lambda-Cold Dark Matter model explains cosmological observations most accurately till date. However, it is still plagued with various shortcomings at galactic scales. Models of dark matter such as superfluid dark matter, Bose-Einstein Condensate(BEC) dark matter and fuzzy dark matter have been proposed to overcome some of these drawbacks. In this work, we probe these models using the current constraint on the gravitational wave (GW) propagation speed coming from the binary neutron star GW170817 detection by LIGO-Virgo detector network and use it to study the allowed parameter space for these three models for Advanced LIGO+Virgo, LISA, IPTA and SKA detection frequencies. The speed of GW has been shown to depend upon the refractive index of the medium, which in turn, depends on the dark matter model parameters through the density profile of the galactic halo. We constrain the parameter space for these models using the bounds coming from GW speed measurement and the Milky Way radius bound. Our findings suggest that with Advanced LIGO-Virgo detector sensitivity, the three models considered here remain unconstrained. A meaningful constraint can only be obtained for detection frequencies ≤ 10-9 Hz, which falls in the detection range of radio telescopes such as IPTA and SKA. Considering this best possible case, we find that out of the three condensate models, the fuzzy dark matter model is the most feasible scenario to be falsified/validated in near future.

Extended Bose–Einstein condensate dark matter in viscous Gauss–Bonnet gravity

In this paper, we study the [Formula: see text] gravity model with an interacting model by flat-FRW metric in a viscous fluid. We consider that the universe dominates with components of dark matter and dark energy. This means that the dark matter component derives from Extended Bose–Einstein Condensate (EBEC) and the components of dark energy arise from the [Formula: see text] gravity. After obtaining the Einstein equation, the energy density and the pressure of dark energy are written in terms of the geometry of the curvature and the Gauss–Bonnet terms, and components of dark matter and viscous fluid. Also, the corresponding continuity equations are written with the presence of interaction terms. In what follows, we employ the EBEC regime instead of the normal dark matter by the dark matter Equation of State (EoS) as [Formula: see text], which arises from the gravitational form. The EoS can be expressed from the perspective of the virial expansion, in which the first and second terms represent normal dark matter and quantum ground state. Next, the corresponding Friedmann equations reconstruct in terms of the redshift parameter, then by using the scenario of the power-law cosmology for the scale factor, we fit the present model with the Hubble amounts of 51 supernova data by the likelihood analysis. In that case, we acquire the cosmological parameters of dark energy in terms of the redshift parameter, and by plotting these graphs, we see that the universe is currently undergoing an accelerated expansion phase. Finally, we investigate the stability of the present model with the sound speed parameter.

Cosmological simulations of self-interacting Bose-Einstein condensate dark matter

Fully 3D cosmological simulations of scalar field dark matter with self-interactions, also known as Bose-Einstein condensate dark matter, are performed using a set of effective hydrodynamic equations. These are derived from the non-linear Schrödinger equation by performing a smoothing operation over scales larger than the de Broglie wavelength, but smaller than the self-interaction Jeans’ length. The dynamics on the de Broglie scale become an effective thermal energy in the hydrodynamic approximation, which is assumed to be subdominant in the initial conditions, but become important as structures collapse and the fluid is shock-heated. The halos that form have Navarro-Frenk-White envelopes, while the centers are cored due to the fluid pressures (thermal + self-interaction), confirming the features found by Dawoodbhoy et al. (2021, MNRAS, 506, 2418) using 1D simulations under the assumption of spherical symmetry. The core radii are largely determined by the self-interaction Jeans’ length, even though the effective thermal energy eventually dominates over the self-interaction energy everywhere, a result that is insensitive to the initial ratio of thermal energy to interaction energy, provided it is sufficiently small to not affect the linear and weakly non-linear regimes. Scaling relations for the simulated population of halos are compared to Milky Way dwarf spheroidals and nearby galaxies, assuming a Burkert halo profile, and are found to not match, although they conform better with observations compared to fuzzy dark matter-only simulations.

Compact stars admitting Finch-Skea symmetry in the presence of various matter fields* *PKS acknowledges National Board for Higher Mathematics (NBHM) under Department of Atomic Energy (DAE), Govt. of India for financial support to carry out the Research project No.: 02011/3/2022 NBHM (R.P.)/R#D II/2152 Dt.14.02.2022. Sokoliuk O. performed the work in frame of the "Mathematical modeling in interdisciplinary research of processes

In the present study, we investigate the anisotropic stellar solutions admitting Finch-Skea symmetry (viable and non-singular metric potentials) in the presence of some exotic matter fields, such as Bose-Einstein Condensate (BEC) dark matter, the Kalb-Ramond fully anisotropic rank-2 tensor field from the low-energy string theory effective action, and the gauge field imposing symmetry. Interior spacetime is matched with both Schwarzchild and Reissner-Nördstrom vacuum spacetimes for BEC, KB, and gauge fields. In addition, we study the energy conditions, Equation of State (EoS), radial derivatives of energy density and anisotropic pressures, Tolman-Oppenheimer-Volkoff equilibrium condition, relativistic adiabatic index, sound speed, and surface redshift. Most of the aforementioned conditions are satisfied. Therefore, the solutions derived in the current study lie in the physically acceptable regime.

Bose–Einstein Condensate dark matter models in the presence of baryonic matter and random confining potentials

We consider the effects of an uncorrelated random potential on the properties of Bose–Einstein Condensate (BEC) dark matter halos, which acts as a source of disorder, and which is added as a new term in the Gross–Pitaevskii equation, describing the properties of the halo. By using the hydrodynamic representation we derive the basic equation describing the density distribution of the galactic dark matter halo, by also taking into account the effects of the baryonic matter, and of the rotation. The density, mass and tangential velocity profiles are obtained exactly in spherical symmetry by considering a simple exponential density profile for the baryonic matter, and a Gaussian type disorder potential. To test the theoretical model we compare its predictions with a set of 39 galaxies from the Spitzer Photometry and Accurate Rotation Curves (SPARC) database. We obtain estimates of the relevant astrophysical parameters of the dark matter dominated galaxies, including the baryonic matter properties, and the parameters of the random potential. The BEC model in the presence of baryonic matter and a random confining potential gives a good statistical description of the SPARC data. The presence of the condensate dark matter could also provide a solution for the core/cusp problem.

A heuristic wave equation parameterizing BEC dark matter halos with a quantum core and an isothermal atmosphere

The Gross–Pitaevskii–Poisson equations that govern the evolution of self-gravitating Bose–Einstein condensates, possibly representing dark matter halos, experience a process of gravitational cooling and violent relaxation. We propose a heuristic parametrization of this complicated process in the spirit of Lynden-Bell’s theory of violent relaxation for collisionless stellar systems. We derive a generalized wave equation that was introduced phenomenologically in Chavanis (Eur Phys J Plus 132:248, 2017) involving a logarithmic nonlinearity associated with an effective temperature $$T_\mathrm{eff}$$ and a damping term associated with a friction $$\xi $$ . These terms can be obtained from a maximum entropy production principle and are linked by a form of Einstein relation expressing the fluctuation-dissipation theorem. The wave equation satisfies an H-theorem for the Lynden-Bell entropy and relaxes towards a stable equilibrium state which is a maximum of entropy at fixed mass and energy. This equilibrium state represents the most probable state of a Bose–Einstein condensate dark matter halo. It generically has a core-halo structure. The quantum core prevents gravitational collapse and may solve the core-cusp problem. The isothermal halo leads to flat rotation curves in agreement with the observations. These results are consistent with the phenomenology of dark matter halos. Furthermore, as shown in a previous paper (Chavanis in Phys Rev D 100:123506, 2019), the maximization of entropy with respect to the core mass at fixed total mass and total energy determines a core mass–halo mass relation which agrees with the relation obtained in direct numerical simulations. We stress the importance of using a microcanonical description instead of a canonical one. We also explain how our formalism can be applied to the case of fermionic dark matter halos.

Constraints on self-interacting Bose-Einstein condensate dark matter using large-scale observables

Constraints on the cosmic history of self-interacting Bose-Einstein condensed (SIBEC) dark matter (DM) are obtained using the cosmic microwave background (CMB), baryonic acoustic oscillations (BAO), growth factor measurements, and type Ia supernovae (SNIa) distances. Four scenarios are considered, one with purely SIBEC-DM, and three in which SIBEC-DM is the final product of some transition from different initial states, which are either cold, warm, or has a constant equation of state. Using a fluid approximation for the self-interacting scalar field it is found that in the simplest scenario of purely SIBEC-DM the self-interaction necessary for solving the cusp-core problem, with core-radii of low-mass halos of order R c ≳ 1kpc, is excluded at 2.4σ, or 98.5% confidence. Introducing a transition, however, relaxes this constraint, but the transitions are preferred to be after matter-radiation equality, and the initial phase to be cold.

Phases of the Bose–Einstein Condensate Dark Matter Model with Both Two- and Three-Particle Interactions

In this paper, we further elaborate on the Bose–Einstein condensate (BEC) dark matter model extended in our previous work [Phys. Rev. D 2020, 102, 083510] by the inclusion of sixth-order (or three-particle) repulsive self-interaction term. Herein, our goal is to complete the picture through adding to the model the fourth-order repulsive self-interaction. The results of our analysis confirm the following: while in the previous work the two-phase structure and the possibility of first-order phase transition was established, here we demonstrate that with the two self-interactions involved, the nontrivial phase structure of the enriched model remains intact. For this to hold, we study the conditions which the parameters of the model, including the interaction parameters, should satisfy. As a by-product and in order to provide some illustration, we obtain the rotation curves and the (bipartite) entanglement entropy for the case of a particular dwarf galaxy.

Jeans mass-radius relation of self-gravitating Bose-Einstein condensates and typical parameters of the dark matter particle

We study the Jeans mass-radius relation of Bose-Einstein condensate dark matter in Newtonian gravity. We show at a general level that it is similar to the mass-radius relation of Bose-Einstein condensate dark matter halos [P.H. Chavanis, Phys. Rev. D {\bf 84}, 043531 (2011)]. Bosons with a repulsive self-interaction generically evolve from the Thomas-Fermi regime to the noninteracting regime as the Universe expands. In the Thomas-Fermi regime, the Jeans radius remains approximately constant while the Jeans mass decreases. In the noninteracting regime, the Jeans radius increases while the Jeans mass decreases. Bosons with an attractive self-interaction generically evolve from the nongravitational regime to the noninteracting regime as the Universe expands. In the nongravitational regime, the Jeans radius and the Jeans mass increase. In the noninteracting regime, the Jeans radius increases while the Jeans mass decreases. The transition occurs at a maximum Jeans mass which is similar to the maximum mass of Bose-Einstein condensate dark matter halos with an attractive self-interaction. We use the mass-radius relation of dark matter halos and the observational evidence of a ``minimum halo'' (with typical radius $R\sim 1\, {\rm kpc}$ and typical mass $M\sim 10^8\, M_{\odot}$) to constrain the mass $m$ and the scattering length $a_s$ of the dark matter particle.

Bose-Einstein condensate dark matter model with three-particle interaction and two-phase structure

We explore the consequences of including the repulsive three-particle interaction in the model of Bose-Einstein condensate dark matter model or fuzzy dark matter. Such a model based on properly modified Gross-Pitaevskii equation is intended to describe the distribution of dark matter particles in the highly dense regions, which correspond to the galaxy core and/or to the overlap of colliding galaxies. Specifically, we deal with the $\phi^6$-model in terms of the macroscopic wave function of the condensate, where a locality of interaction is guaranteed by a large correlation length assumed to hold. After calculation of main thermodynamical characteristics, we find strong evidence of the existence of two distinct phases of dark matter, within its core, separated by the instability region lying between two differing special values of the pressure acting in the model. Some implications stemming from the existence of two phases and the related first-order phase transition are discussed.

The M-sigma relation of supermassive black holes from the scalar field dark matter

We show a relation between the mass of supermassive black holes in galaxies and the velocity dispersions of their bulges in the scalar field or the Bose–Einstein condensate dark matter model. The gravity of the central black holes changes boundary conditions of the scalar field at the galactic centers. Owing to the wave nature of the dark matter, this significantly changes the galactic dark matter halo profiles even though the black holes are much lighter than the bulges. As a result the heavier the black holes are, the more compact the bulges are, and hence the larger the velocity dispersions are. This tendency is verified by a numerical study showing the M-sigma relation reproduced with the dark matter particle mass [Formula: see text] eV.

Partition function of the Bose–Einstein condensate dark matter and the modified Gross–Pitaevskii equation

Intending to describe the dark matter (DM) of dwarf galaxies, we concentrate on one model of the slowly rotating and gravitating Bose–Einstein condensate (BEC). For a deeper understanding of its properties, we calculate the partition function and compare the characteristics derived from it with the results based on the solution of Gross–Pitaevskii equation (GPE). In our approach, which uses Green’s functions of spatial evolution operators, we formulate in a unified way the boundary conditions, important for applying the Thomas–Fermi approximation. Taking this into account, we revise some of the results obtained earlier. We also derive the spatial particle distribution, similar to the model with rotation, by using the deformation of commutation relations for a macroscopic wave function and modifying the GPE. It is shown that such an approach leads to the entropy inhomogeneity and makes the distribution dependent on temperature.

Predictive model of BEC dark matter halos with a solitonic core and an isothermal atmosphere

We develop a model of Bose-Einstein condensate dark matter halos with a solitonic core and an isothermal atmosphere based on a generalized Gross-Pitaevskii-Poisson equation [P.H. Chavanis, Eur. Phys. J. Plus 132, 248 (2017)]. This equation provides a heuristic coarse-grained parametrization of the ordinary Gross-Pitaevskii-Poisson equation accounting for violent relaxation and gravitational cooling. It involves a cubic nonlinearity taking into account the self-interaction of the bosons, a logarithmic nonlinearity associated with an effective temperature, and a source of dissipation. It leads to superfluid dark matter halos with a core-halo structure. The quantum potential or the self-interaction of the bosons generates a solitonic core that solves the cusp problem of the cold dark matter model. The logarithmic nonlinearity generates an isothermal atmosphere accounting for the flat rotation curves of the galaxies. The dissipation ensures that the system relaxes towards an equilibrium configuration. In the Thomas-Fermi approximation, the dark matter halo is equivalent to a barotropic gas with an equation of state $P=2\pi a_s\hbar^2\rho^2/m^3+\rho k_B T/m$, where $a_s$ is the scattering length of the bosons and $m$ is their individual mass. We numerically solve the equation of hydrostatic equilibrium and determine the corresponding density profiles and rotation curves. Our model has no free parameter so it is completely predictive. Extension of this model to noninteracting bosons and fermions will be presented in forthcoming papers.

On the possibility of wormhole formation in the galactic halo due to dark matter Bose–Einstein condensates

It has been recently claimed that dark matter could be in the form of a Bose-Einstein condensate (BEC) in order to explain the dynamics at large distances from the galactic center [Boehmer, Harko, JCAP {\bf 0706}, 025 (2007)]. In this paper we explore the possibility of wormhole formation in galactic halos due to the dark matter BEC. In particular we have found a new wormhole solution supported by BEC dark matter using the expressions for the density profile of the BEC and rotation velocity along with the Einstein field equations to calculate the wormhole red shift function as well as the shape function. To this end, we show that for a specific choose of the central density of the condensates our wormhole solution satisfies the flare our condition. Furthermore we check the null, weak, and strong condition at the wormhole throat with a radius $r_0$, and shown that in general the energy condition are violated by some arbitrary quantity at the wormhole throat. Using the volume integral quantifier, and choosing reasonable values of parameters we have calculate the amount of BEC exotic matter near the wormhole throat, such that the wormhole extends form $r_0$ to a a cut off radius situated at $`a'$. Moreover we have introduced a Kerr-like metric for a rotating BEC wormhole to study the effect of BEC dark matter on the Lense-Thirring precession frequencies. Namely, we have shown that the obtained precession frequencies lie within a range of typical quasi-periodic oscillations (QPOs).

New predictions from the logotropic model

Abstract In a previous paper (Chavanis, 2015) we have introduced a new cosmological model that we called the logotropic model. This model involves a fundamental constant Λ which is the counterpart of Einstein’s cosmological constant in the Λ CDM model. The logotropic model is able to account, without free parameter, for the constant surface density of the dark matter halos, for their mass–radius relation, and for the Tully–Fisher relation. In this paper, we explore other consequences of this model. By advocating a form of “strong cosmic coincidence” we predict that the present proportion of dark energy in the Universe is Ω de,0 = e ∕ ( 1 + e ) ≃ 0 . 731 which is close to the observed value. We also remark that the surface density of dark matter halos and the surface density of the Universe are of the same order as the surface density of the electron. This makes a curious connection between cosmological and atomic scales. Using these coincidences, we can relate the Hubble constant, the electron mass and the electron charge to the cosmological constant. We also suggest that the famous numbers 137 (fine-structure constant) and 123 (logotropic constant) may actually represent the same thing. This could unify microphysics and cosmophysics. We study the thermodynamics of the logotropic model and find a connection with the Bekenstein–Hawking entropy of black holes if we assume that the logotropic dark fluid is made of particles of mass m Λ ∼ ħ Λ ∕ c 2 = 2 . 08 × 1 0 − 33 eV∕c 2 (cosmons). In that case, the universality of the surface density of the dark matter halos may be related to a form of holographic principle (the fact that their entropy scales like their area). We use similar arguments to explain why the surface density of the electron and the surface density of the Universe are of the same order and justify the empirical Weinberg relation. Finally, we combine the results of our approach with the quantum Jeans instability theory to predict the order of magnitude of the mass of ultralight axions m ∼ 1 0 − 23 eV∕c 2 in the Bose–Einstein condensate dark matter paradigm.

Derivation of a generalized Schrödinger equation for dark matter halos from the theory of scale relativity

Abstract Using Nottale’s theory of scale relativity, we derive a generalized Schrodinger equation applying to dark matter halos. This equation involves a logarithmic nonlinearity associated with an effective temperature and a source of dissipation. Fundamentally, this wave equation arises from the nondifferentiability of the trajectories of the dark matter particles whose origin may be due to ordinary quantum mechanics, classical ergodic (or almost ergodic) chaos, or to the fractal nature of spacetime at the cosmic scale. The generalized Schrodinger equation involves a coefficient D , possibly different from ħ ∕ 2 m (where ħ is the Planck constant and m the mass of the particles), whose value for dark matter halos is D = 1 . 02 × 1 0 23 m2/s. This model is similar to the Bose–Einstein condensate dark matter model except that it does not require the dark matter particle to be ultralight. It can accommodate any type of particles provided that they have nondifferentiable trajectories. We suggest that the cold dark matter crisis may be solved by the fractal (nondifferentiable) structure of spacetime at the cosmic scale, or by the chaotic motion of the particles on a very long timescale, instead of ordinary quantum mechanics. The equilibrium states of the generalized Schrodinger equation correspond to configurations with a core-halo structure. The quantumlike potential generates a solitonic core that solves the cusp problem of the classical cold dark matter model. The logarithmic nonlinearity accounts for the presence of an isothermal halo that leads to flat rotation curves (it also accounts for the isothermal core of large dark matter halos). The damping term ensures that the system relaxes towards an equilibrium state. This property is guaranteed by an H -theorem satisfied by a Boltzmann-like free energy functional. In our approach, the temperature and the friction arise from a single formalism. They correspond to the real and imaginary parts of the complex friction coefficient present in the scale covariant equation of dynamics that is at the basis of Nottale’s theory of scale relativity. They may be the manifestation of a cosmic aether or the consequence of a process of violent relaxation and gravitational cooling on a coarse-grained scale.

Magnification Bias of Distant Galaxies in the Hubble Frontier Fields: Testing Wave Versus Particle Dark Matter Predictions

Abstract Acting as powerful gravitational lenses, the strong lensing galaxy clusters of the deep Hubble Frontier Fields (HFF) program permit access to lower-luminosity galaxies lying at higher redshifts than hitherto possible. We analyzed the HFF to measure the volume density of Lyman-break galaxies at z > 4.75 by identifying a complete and reliable sample up to z ≃ 10. A marked deficit of such galaxies was uncovered in the highly magnified regions of the clusters relative to their outskirts, implying that the magnification of the sky area dominates over additional faint galaxies magnified above the flux limit. This negative magnification bias is consistent with a slow rollover at the faint end of the UV luminosity function and it indicates a preference for Bose–Einstein condensate dark matter with a light boson mass of m B ≃ 10 − 22 eV over standard cold dark matter. We emphasize that measuring the magnification bias requires no correction for multiply-lensed images (with typically three or more images per source), whereas directly reconstructing the luminosity function will lead to an overestimate unless such images can be exhaustively matched up, especially at the faint end that is only accessible in the strongly lensed regions. In addition, we detected a distinctive downward transition in galaxy number density at z ≳ 8, which may be linked to the relatively late reionization reported by Planck. Our results suggests that JWST will likely peer into an “abyss” with essentially no galaxies detected in deep NIR imaging at z > 10.