When a gas of bosonic particles is cooled below a critical temperature, it condenses into a Bose-Ei…

Bose-Einstein condensation

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Principles Of Physical Cosmology

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

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

In this paper, we study the local observational consequences of a violation of the Einstein Equivalence Principle induced by models of light scalar Dark Matter (DM). We focus on two different models where the scalar field couples linearly or quadratically to the standard model of matter fields. For both these cases, we derive the solutions of the scalar field. We also derive from first principles the expressions for two types of observables: (i) the local comparison of two atomic sensors that are differently sensitive to the constants of Nature and (ii) the local differential acceleration between two test masses with different compositions. For the linear coupling, we recover that the signatures induced by DM on both observables are the sum of harmonic and Yukawa terms. For the quadratic coupling on the other hand, the signatures derived for both types of observables turn out to be the sum of a time-independent term and a harmonic oscillation, whose amplitudes both depend on the position. Such behavior is new and can make experiments in space more sensitive than terrestrial ones. Besides this, the observables present some interesting nonlinear behaviors that are due to the amplification or to the screening of the scalar field, depending on the parameters of the theory, and on the compactness of the source of the gravitational field. Finally, we infer the various limits on the DM coupling parameters by using existing frequency comparisons on the one hand and tests of the universality of free fall on the ground (torsion balances) or in space (MICROSCOPE mission) on the other hand. We show that in the quadratic case, so-called natural parameters are still allowed by observations.

Violation of the equivalence principle from light scalar dark matter

Beyond Einstein gravity

In this article we perform a second order perturbation analysis of the gravitational metric theory of gravity f(χ) = χ 3/2 developed by Bernal et al. (2011). We show that the theory accounts in detail for two observational facts: (1) the phenomenology of flattened rotation curves associated to the Tully-Fisher relation observed in spiral galaxies, and (2) the details of observations of gravitational lensing in galaxies and groups of galaxies, without the need of any dark matter. We show how all dynamical observations on flat rotation curves and gravitational lensing can be synthesised in terms of the empirically required metric coefficients of any metric theory of gravity. We construct the corresponding metric components for the theory presented at second order in perturbation, which are shown to be perfectly compatible with the empirically derived ones. It is also shown that under the theory being presented, in order to obtain a complete full agreement with the observational results, a specific signature of Riemann’s tensor has to be chosen. This signature corresponds to the one most widely used nowadays in relativity theory. Also, a computational program, the MEXICAS (Metric EXtended-gravity Incorporated through a Computer Algebraic System) code, developed for its usage in the Computer Algebraic System (CAS) Maxima for working out perturbations on a metric theory of gravity, is presented and made publicly available.

Gravitational lensing with $ f(χ)=χ^{3/2} $ gravity in accordance with astrophysical observations

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.

Scalar field dark matter in clusters of galaxies

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.

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

Classical solutions of the Klein–Gordon equation are used in astrophysics to model galactic halos of scalar field dark matter and compact objects such as cores of neutron stars. These bound solutions are interpreted as Bose–Einstein condensates whose particle number density is governed by the Gross–Pitaevskii (GP) equation. It is well known that the Gross–Pitaevskii–Poisson (GPP) system arises as the non-relativistic limit of the Klein–Gordon–Einstein (KGE) equations and, conversely, the KGE system may be interpreted as a generalization of the GPP equations in a curved space-time. In the present work, we consider a 3+1 ADM foliation of the space-time in order to construct a general-relativistic version of the GP equation. Besides, we derive a general energy balance equation for the boson gas in the hydrodynamic variables, where different energy potentials are identified as kinetic, quantum, electromagnetic and gravitational. In addition, we find a correspondence between the energy potentials in the balance equation and actual components of the scalar energy–momentum tensor. We also study the Newtonian limit of the hydrodynamic formulation and the balance equation. As an illustrative case, we study the effects in the energy potentials of a relativistic correction in the GP equation.

Energy balance of a Bose gas in a curved space-time

We derive a general energy balance equation for a self-interacting boson gas at vanishing temperature in a curved spacetime. This represents a first step towards a formulation of the first law of thermodynamics for a scalar field in general relativity. By using a $3+1$ foliation of the spacetime and performing a Madelung transformation, we rewrite the Klein-Gordon-Maxwell equations in a general curved spacetime into its hydrodynamic version where we can identify the different energy contributions of the system and separate them into kinetic, quantum, electromagnetic, and gravitational.

Tula Bernal

Papers

Gravitational lensing with $ f(χ)=χ^{3/2} $ gravity in accordance with astrophysical observations

Scalar field dark matter in clusters of galaxies

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

Energy balance of a Bose gas in a curved space-time

Energy Balance of a Bose Gas in Curved Spacetime