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The measurements of the CMB have determined the cosmological parameters with high accuracy, and the observation of the flatness of space have contributed to the status of the concordance $\Lambda$CDM model. However, the cosmological constant $\Lambda$, necessary to close the model to critical density, remains an open conundrum. We explore the observed late-time accelerated expansion of the Universe, where we consider that the Friedmann equation describes the expansion history of FLRW universes in the local reference frame of freely falling comoving observers, which perceive flat, homogeneous and isotropic space in their local inertial system, where, as a consequence of the equivalence principle, special relativity applies. We use this fact to propose an extension to $\Lambda$CDM, incorporating the initial conditions of the background universe, comprising the initial energy densities as well as the initial post big bang expansion rate. The observed late-time accelerated expansion is then attributed to a kinematic effect akin to a dark energy component. Choosing the same $\Omega_{m,0} \simeq 0.3$ as $\Lambda$CDM, its equation of state $w_{de} \simeq -0.8$. Furthermore, we include the impact on the expansion history caused by the cosmic web of the late Universe, once voids dominate its volume, and find that the initially constant $w_{de}$ becomes time-dependent, evolving to a value of $w_{de} \simeq -0.9$ at the present. While this impact by voids is minor, it is sufficient to provide a solution to the Hubble tension problem. We use CLASS to calculate the expansion history and power spectra of our extension and compare our results to concordance $\Lambda$CDM and to observations. We find that our model agrees well with current data, in particular with the final data release PR4 of the Planck mission, where it explains the reported spatial curvature of $\Omega_{k,0} = - 0.012 \pm 0.010$., Comment: 18 Pages, 8 Figures

(abridged)Scalar field dark matter (SFDM) made of bosons has become a popular alternative to the CDM paradigm, especially for its potential to cure the so-called "small-scale problems" of CDM. Cosmological simulations have determined that SFDM halos exhibit a core-envelope structure, but they are computationally expensive. Halo cores have been found to be well approximated by "solitons". The study of single soliton and multiple soliton merger dynamics constitutes a more feasible approach to investigate in detail the genuine quantum dynamics of SFDM and its interplay with self-gravity for a multitude of free boson parameters. In this paper, we present dedicated simulations of single solitons and binary soliton mergers, for models without and with a 2-boson, repulsive, weak to intermediate self-interaction (SI), as well as multiple soliton mergers without SI. We adapt the open-source code Pyultralight to simulate solitons with SI and make our amended code public. We derive numerical scaling relations between the central density and mass of solitons for several values of SI and find deviations from the monotonic relations known from fuzzy dark matter (no SI), or the strongly repulsive Thomas-Fermi regime. Solitons with SI exemplify larger cores and lower central densities, compared to solitons without SI. Using our simulations, we extract numerical density profiles for solitons and postmerger objects, and fit them to analytical functions of previous literature. We find a mild preference for Gaussian cores for objects with SI, while the envelopes of postmergers can be fit to NFW profiles albeit with some caution as we discuss. Similar to previous work, we find global, persistent oscillations for solitons as well as postmergers, confirming that self-gravitating SFDM has very long relaxation times, although objects with SI exhibit oscillations of comparatively smaller amplitude., Comment: 37 pages, 23 figures; in press with PRD; post-review, revised version includes more explanations, references and new Appendix B. Link to amended code is provided

(abridged)Cosmological observational programs often compare their data not only with $\Lambda$CDM, but also with extensions applying dynamical models of dark energy (DDE), with a time-dependent equation of state (EoS) parameter $w$. We found a degeneracy in the customary computational procedure for the expansion history, once DDE models are applied. This degeneracy provides an infinite number of cosmological models reproducing the Planck-measured CMB spectrum. Moreover, this degeneracy biases the comparison of $\Lambda$CDM with DDE extensions. We present a complementary computational approach, which breaks this degeneracy: the ``fixed early densities (EDs) approach'' evolves cosmological models from the early Universe to the present, in contrast to the customary ``fixed $H_0$ approach'' which evolves cosmological models in reverse order. We find the EDs are accurately approximated by the $\Lambda$CDM model. We implement a refined procedure, appyling both approaches, in an amended version of the code CLASS, where we focus on representative DDE models using the CPL parametrization. Our results reveal that the CPL model $w(a)=-0.9 + 0.1(1-a)$ could provide a resolution to the Hubble tension problem. Moreover, we find that combining both approaches, while requesting to yield consistent results and being in agreement with observations across cosmic time, can serve as a kind of consistency check for cosmological models. Moreover, our proposed consistency check applied within current data analysis methods will increase the accuracy of inferred cosmological parameters significantly, in particular for $\Lambda$CDM extensions. We find characteristic signatures in the late expansion histories of cosmological models, allowing a phenomenological discrimination of DE candidates and a possible resolution of the Hubble tension, by ongoing and future observational programs., Comment: submitted to A&A, 21 pages, 12 figures, published online 12 June 2024

(abridged) We present simulations of halo formation and evolution in scalar field dark matter (SFDM) cosmologies in the Thomas-Fermi regime, aka ``SFDM-TF", where a strong repulsive 2-particle self-interaction (SI) is included, being a valuable alternative to CDM, with the potential to resolve its ``cusp-core" problem. In general, SFDM behaves like a quantum fluid. Previous literature has presented two fluid approximations for SFDM-TF, as well as simulations of halo formation. These results confirmed earlier expectations and are generally in mutual agreement, but discrepancies were also reported. Therefore, we perform dedicated 3D cosmological simulations for the SFDM-TF model, applying both fluid approximations, as well as for CDM. Our results are very well in accordance with previous works and extend upon them, in that we can explain the reported discrepancies as a result of different simulation setups. We find some interesting details: The evolution of both SFDM-TF and CDM halos follows a 2-stage process. In the early stage, the density profile in the center becomes close to a $(n=1.5)$-polytropic core, dominated by an "effective" velocity-dispersion pressure $P_{\sigma}$ which is common to both dark matter models. Consecutively, for CDM halos, the core transitions into a central cusp. In SFDM-TF halos, the additional pressure $P_\text{SI}$ due to SI determines the second stage of the evolution, where the central region follows closely a $(n=1)$-polytropic core, embedded in a nearly isothermal envelope, i.e. the outskirts are similar to CDM. We also encounter a new effect, namely a late-time expansion of both polytropic core plus envelope, because the size of the almost isothermal halo envelope is affected by the expansion of the background universe. So, an initial primordial core of $\sim 100$ pc can evolve into a larger core of $\gtrsim 1$ kpc, even without feedback from baryons., Comment: final version; 26 pages, 16 figures

Bose-Einstein-condensed dark matter (BEC-DM), also called scalar field dark matter (SFDM), has become a popular alternative to the standard, collisionless cold dark matter (CDM) model, due to its long-held potential to resolve the small-scale crisis of CDM. Halos made of BEC-DM have been modelled using the Gross-Pitaevskii (GP) equation coupled to the Poisson equation; the so-called GPP equations of motion. These equations are based on fundamental microphysical conditions that need to be fulfilled in order for the equations to be valid in the first place, related to the diluteness of the DM gas and the nature of the particle scattering model. We use these conditions in order to derive the implications for the BEC-DM parameters, the 2-particle self-interaction coupling strength $g$ and the particle mass $m$. We compare the derived bounds with the constraint that results from the assumption of virial equilibrium of the central cores of halos, deriving a relationship that connects $g$ and $m$. We find that the GPP conditions are greatly fulfilled, for BEC-DM particle masses of interest, if such models also obey the virial condition that turns out to be the strongest constraint. We also derive the implications for the elastic scattering cross section (per particle mass) in BEC-DM halos, based on the scattering model of GPP, and find a huge range of possible values, depending on the self-interaction regime. We put our results into context to recent literature which predicts sub-kpc core size in BEC-DM halos., Comment: 24 pages; 3 figures; revised version which includes more explanations and references and an expanded Figure 1

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

Bose-Einstein-condensed dark matter, also called scalar-field dark matter (SFDM), has become a popular alternative to cold dark matter (CDM), because it predicts galactic cores, in contrast to the cusps of CDM halos ("cusp-core problem"). We continue the study of SFDM with a strong, repulsive self-interaction; the Thomas-Fermi regime of SFDM (SFDM-TF). In this model, structure formation is suppressed below a scale related to the TF radius $R_\text{TF}$, which is close to the radius of central cores in these halos. We investigate for the first time the impact of baryons onto realistic galactic SFDM-TF halo profiles by studying the process of adiabatic contraction (AC) in such halos. In doing so, we first analyse the underlying quantum Hamilton-Jacobi framework appropriate for SFDM and calculate dark matter orbits, in order to verify the validity of the assumptions usually required for AC. Then, we calculate the impact of AC onto SFDM-TF halos of mass $\sim 10^{11}~M_{\odot}$, with various baryon fractions and core radii, $R_\text{TF} \sim (0.1 - 4)$ kpc, and compare our results with observational velocity data of dwarf galaxies. We find that AC-modified SFDM-TF halos with kpc-size core radii reproduce the data well, suggesting stellar feedback may not be required. On the other hand, halos with sub-kpc core radii face the same issue than CDM, in that they are not in accordance with galaxy data in the central halo parts., Comment: minor revisions, accepted by MNRAS; 20 pages, 9 figures

Scalar Field Dark Matter (SFDM) comprised of ultralight ($\gtrsim 10^{-22}$ eV) bosons is an alternative to standard, collisionless Cold Dark Matter (CDM) that is CDM-like on large scales but inhibits small-scale structure formation. As a Bose-Einstein condensate, its free-field ("fuzzy") limit (FDM) suppresses structure below the de Broglie wavelength, $\lambda_\text{deB}$, creating virialized haloes with central cores of radius $\sim\lambda_\text{deB}$, surrounded by CDM-like envelopes, and a halo mass function (HMF) with a sharp cut-off on small scales. With a strong enough repulsive self-interaction (SI), structure is inhibited, instead, below the Thomas-Fermi (TF) radius, $R_\text{TF}$ (the size of an SI-pressure-supported ($n=1$)-polytrope), when $R_\text{TF} > \lambda_\text{deB}$. Previously, we developed tools to describe SFDM dynamics on scales above $\lambda_\text{deB}$ and showed that SFDM-TF haloes formed by Jeans-unstable collapse from non-cosmological initial conditions have $R_\text{TF}$-sized cores, surrounded by CDM-like envelopes. Revisiting SFDM-TF in the cosmological context, we simulate halo formation by cosmological infall and collapse, and derive its transfer function from linear perturbation theory to produce cosmological initial conditions and predict statistical measures of structure formation, such as the HMF. Since FDM and SFDM-TF transfer functions both have small-scale cut-offs, we can align them to let observational constraints on FDM proxy for SFDM-TF, finding FDM with particle masses $1 \lesssim m/(10^{-22} \text{ eV}/c^2) \lesssim 30$ corresponds to SFDM-TF with $10 \gtrsim R_\text{TF}/(1 \text{ pc}) \gtrsim 1$, favoring sub-galactic (sub-kpc) core-size. The SFDM-TF HMF cuts off gradually, however, leaving more small-mass haloes: its Jeans mass shrinks so fast, scales filtered early can still recover and grow!, Comment: 30 pages, 10 figures, accepted by MNRAS 09/22/21, comments welcome

In recent years, Bose-Einstein-condensed dark matter (BEC-DM) has become a popular alternative to standard, collisionless cold dark matter (CDM). This BEC-DM - also called scalar field dark matter (SFDM) - can suppress structure formation and thereby resolve the small-scale crisis of CDM for a range of boson masses. However, these same boson masses also entail implications for BEC-DM substructure within galaxies, especially within our own Milky Way. Observational signature effects of BEC-DM substructure depend upon its unique quantum-mechanical features and have the potential to reveal its presence. Ongoing efforts to determine the dark matter substructure in our Milky Way will continue and expand considerably over the next years. In this contribution, we will discuss some of the existing constraints and potentially new ones with respect to the impact of BEC-DM onto baryonic tracers. Studying dark matter substructure in our Milky Way will soon resolve the question, whether dark matter behaves classical or quantum on scales of $\lesssim 1$ kpc., Comment: 23 pages; post-proof version, minor revisions (some more discussion on cosmological bounds and microlensing; substantially expanded list of references); invited article to Frontiers in Astronomy and Space Sciences, within the Research Topic "When Planck, Einstein and Vera Rubin meet. Dark Matter: What is it? Where is it?"

Scalar Field Dark Matter (SFDM) comprised of ultralight bosons has attracted great interest as an alternative to standard, collisionless Cold Dark Matter (CDM) because of its novel structure-formation dynamics, described by the coupled Schr\"odinger-Poisson equations. In the free-field ("fuzzy") limit of SFDM (FDM), structure is inhibited below the de Broglie wavelength, but resembles CDM on larger scales. Virialized haloes have "solitonic" cores of radius $\sim\lambda_\text{deB}$, surrounded by CDM-like envelopes. When a strong enough repulsive self-interaction (SI) is also present, structure can be inhibited below a second length scale, $\lambda_\text{SI}$, with $\lambda_\text{SI}> \lambda_\text{deB}$ -- called the Thomas-Fermi (TF) regime. FDM dynamics differs from CDM because of quantum pressure, and SFDM-TF differs further by adding SI pressure. In the small-$\lambda_\text{deB}$ limit, however, we can model all three by fluid conservation equations for a compressible, $\gamma=5/3$ ideal gas, with ideal gas pressure sourced by internal velocity dispersion and, for the TF regime, an added SI pressure, $P_\text{SI}\propto \rho^2$. We use these fluid equations to simulate halo formation from gravitational collapse in 1D, spherical symmetry, demonstrating for the first time that SFDM-TF haloes form with cores the size of $R_\text{TF}$, the radius of an SI-pressure-supported $(n=1)$-polytrope, surrounded by CDM-like envelopes. In comparison with rotation curves of dwarf galaxies in the local Universe, SFDM-TF haloes pass the ["too-big-to-fail" + "cusp-core"]-test if $R_\text{TF}\gtrsim 1$ kpc., Comment: 27 pages, 11 figures, accepted by MNRAS 06/28/21, comments welcome

Scalar Field Dark Matter (SFDM), comprised of ultralight ($\gtrsim 10^{-22}$ eV) bosons, is distinguished from massive ($\gtrsim$ GeV), collisionless Cold Dark Matter (CDM) by its novel structure-formation dynamics as Bose-Einstein condensate (BEC) and quantum superfluid with wave-like properties, described by the Gross-Pitaevski and Poisson (GPP) equations. In the free-field (fuzzy) limit of SFDM (FDM), structure is inhibited below the de Broglie wavelength $\lambda_{\text{deB}}$, but resembles CDM on larger scales. Virialized haloes have solitonic cores of radius $\sim \lambda_{\text{deB}}$ that follow the ground-state attractor solution of GPP, surrounded by CDM-like envelopes. As superfluid, SFDM is irrotational (vorticity-free) but can be unstable to vortex formation. We previously showed this can happen in halo cores, from angular momentum arising during structure formation, when repulsive self-interaction (SI) is present to support them out to a second length scale $\lambda_{\text{SI}}$ with $\lambda_{\text{SI}} > \lambda_{\text{deB}}$ (the Thomas-Fermi regime), but only if SI is strong enough. This suggested FDM cores (without SI) would not form vortices. FDM simulations later found vortices, but only outside halo cores, consistent with our previous suggestion based upon TF-regime analysis. We extend that analysis now to FDM, to show explicitly that vortices should not arise in solitonic cores from angular momentum, modelling them as either Gaussian spheres or compressible, ($n = 2$)-polytropic, irrotational Riemann-S ellipsoids. We find that, for typical halo spin parameters, angular momentum per particle is below $\hbar$, the minimum required even for one singly-quantized vortex in the centre. Even for larger angular momentum, however, vortex formation is not energetically favoured., Comment: accepted by MNRAS, 29 pages, 9 figures; minor revisions

The first bright objects to form in the Universe might not have been "ordinary" fusion-powered stars, but "Dark Stars" (DSs) powered by the annihilation of dark matter (DM) in the form of Weakly Interacting Massive Particles (WIMPs). If discovered, DSs can provide a unique laboratory to test DM models. DSs are born with a mass of order $M_\odot$ and may grow to a few million solar masses; in this work we investigate the properties of early DSs with masses up to $\sim \! 1000 \, M_\odot$, fueled by WIMPS weighing $100$ GeV. We improve the previous implementation of the DM energy source into the stellar evolution code MESA. We show that the growth of DSs is not limited by astrophysical effects: DSs up to $\sim \! 1000 \, M_\odot$ exhibit no dynamical instabilities; DSs are not subject to mass-loss driven by super-Eddington winds. We test the assumption of previous work that the injected energy per WIMP annihilation is constant throughout the star; relaxing this assumption does not change the properties of the DSs. Furthermore, we study DS pulsations, for the first time investigating non-adiabatic pulsation modes, using the linear pulsation code GYRE. We find that acoustic modes in DSs of masses smaller than $\sim \! 200 \, M_\odot$ are excited by the $\kappa-\gamma$ and $\gamma$ mechanism in layers where hydrogen or helium is (partially) ionized. Moreover, we show that the mass-loss rates potentially induced by pulsations are negligible compared to the accretion rates., Comment: minor revisions; accepted by MNRAS; 15 pages, 6 Figures

Scalar-field dark matter (SFDM) halos exhibit a core-envelope structure with soliton-like cores and CDM-like envelopes. Simulations without self-interaction (free-field case) report a core-halo mass relation $M_c\propto M_{h}^{\beta}$, with either $\beta=1/3$ or $\beta=5/9$, which can be understood if core and halo obey certain energy or velocity scalings. We extend the core-halo mass relations to include SFDM with self-interaction (SI), either repulsive or attractive, and investigate its implications for the gravitational instability and collapse of solitonic cores, leading to supermassive black hole (SMBH) formation. For SFDM parameters that make $\sim$ Kpc-sized cores and CDM-like structure formation on large scales but suppressed on small scales, cores are stable for all galactic halos of interest, from the free-field to the repulsive SI limit. For attractive SI, however, halos masses $M_h\sim (10^{10}-10^{12}) M_\odot$ have cores that collapse to SMBHs with $M_{SMBH}\sim 10^{6}-10^8 M_\odot$, as observations seem to require, while smaller-mass halos have stable cores, for particle masses $m\simeq (2.14\times 10^{-22}-9.9\times 10^{-20})\rm{eV}/c^2$, if the free-field has $\beta=1/3$, or $m = 2.23\times 10^{-21}-1.7\times 10^{-18}\rm{eV}/c^2$, if $\beta=5/9$. For free-field and repulsive cases, however, if previous constraints on particle parameters are relaxed to allow much smaller (sub-galactic scale) cores, then halos can also form SMBHs, for the same range of halo and BH masses, as long as $\beta = 5/9$ is correct for the free-field. In that case, structure formation in SFDM would be largely indistinguishable from Cold Dark Matter (CDM). Such SFDM models might not resolve the small-scale structure problems of CDM, but they would explain the formation of SMBHs quite naturally. Since CDM, itself, has not yet been ruled out, such SFDM models must also be viable (Abbreviated)., Comment: 27 pages, 7 figures, minor updates to accord with the published version in Phys. Rev. D

Every cosmology lecturer these days is confronted with teaching the modern cosmological standard model $\Lambda$CDM, and there are many approaches to do this. However, the danger is imminent that it is presented to students as something set into stone, merely to be accepted as a fact based on the plenty of evidences we have. This is even more critical, given that the standard model of cosmology confronts us with entities not yet fully understood, namely a cosmological constant $\Lambda$ and cold dark matter. In this article, we report on an advanced cosmology course exercise, conducted in computer lab, which was conceived as a means to have students experience first-hand why the $\Lambda$CDM model has become so prevalent in the interpretation of modern cosmological data. To this end, we focused on the cosmic microwave background radiation (CMB) and calculated theoretical temperature and matter power spectra, using the modern Boltzmann code CLASS. By comparing and analyzing the outcome for $\Lambda$CDM, as well as for three other exotic cosmological models, the students were able to grasp the impact of cosmological parameters on CMB observables, and also to understand some of the complicated CMB physics in a direct way. Our chosen examples are not exhaustive and can be easily modified or expanded, so we express the hope that this article will serve as a valuable resource for interested students and lecturers., Comment: Proof-read, final version; accepted by European Journal of Physics; 21 pages, 5 figures

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

We study the impact on electroweak baryogenesis from a swifter cosmological expansion induced by dark matter. We detail the experimental bounds that one can place on models that realize it, and we investigate the modifications of these bounds that result from a non-standard cosmological history. The modifications can be sizeable if the expansion rate of the Universe increases by several orders of magnitude. We illustrate the impact through the example of scalar field dark matter, which can alter the cosmological history enough to enable a strong-enough first-order phase transition in the Standard Model when it is supplemented by a dimension six operator directly modifying the Higgs boson potential. We show that due to the modified cosmological history, electroweak baryogenesis can be realized, while keeping deviations of the triple Higgs coupling below HL-LHC sensitivies. The required scale of new physics to effectuate a strong-enough first order phase transition can change by as much as twenty percent as the expansion rate increases by six orders of magnitude.

The cosmic evolution of a dark matter model which behaves relativistically in the early Universe is explored. Dark matter is described as a complex scalar field, whose earliest evolution is characterized by a stiff equation of state ($p \simeq \rho$). In this phase, it is the dominant component in the Universe. We present constraints from Big Bang nucleosynthesis and primordial gravity waves from inflation. Also, we study how the associated enhanced expansion rate due to the stiff phase might facilitate a first-order electroweak symmetry breaking phase transition, in light of the recently measured value of the Higgs boson mass., Comment: Presentation at the DPF2015 Meeting of the American Physical Society Division of Particles and Fields, Ann Arbor, Michigan, August 4-8, 2015; 8 pages; 3 figures

Dark Stars are stellar objects made (almost entirely) of hydrogen and helium, but powered by the heat from Dark Matter annihilation, rather than by fusion. They are in hydrostatic and thermal equilibrium, but with an unusual power source. Weakly Interacting Massive Particles (WIMPs), among the best candidates for dark matter, can be their own antimatter and can annihilate inside the star, thereby providing a heat source. Although dark matter constitutes only $\lesssim 0.1\%$ of the stellar mass, this amount is sufficient to power the star for millions to billions of years. Thus, the first phase of stellar evolution in the history of the Universe may have been dark stars. We review how dark stars come into existence, how they grow as long as dark matter fuel persists, and their stellar structure and evolution. The studies were done in two different ways, first assuming polytropic interiors and more recently using the MESA stellar evolution code; the basic results are the same. Dark stars are giant, puffy ($\sim$ 10 AU) and cool (surface temperatures $\sim$10,000 K) objects. We follow the evolution of dark stars from their inception at $\sim 1 M_\odot$ as they accrete mass from their surroundings to become supermassive stars, some even reaching masses $> 10^6 M_\odot$ and luminosities $>10^{10} L_\odot$, making them detectable with the upcoming James Webb Space Telescope. Once the dark matter runs out and the dark star dies, it may collapse to a black hole; thus dark stars may provide seeds for the supermassive black holes observed throughout the Universe and at early times. Other sites for dark star formation may exist in the Universe today in regions of high dark matter density such as the centers of galaxies. The current review briefly discusses dark stars existing today, but focuses on the early generation of dark stars., Comment: 45 pages; 13 Figures; revised and expanded version of an invited review for Reports on Progress in Physics

We use the stellar evolution code MESA to study dark stars. Dark stars (DSs), which are powered by dark matter (DM) self-annihilation rather than by nuclear fusion, may be the first stars to form in the Universe. We compute stellar models for accreting DSs with masses up to 10^6 M_{sun}. The heating due to DM annihilation is self-consistently included, assuming extended adiabatic contraction of DM within the minihalos in which DSs form. We find remarkably good overall agreement with previous models, which assumed polytropic interiors. There are some differences in the details, with positive implications for observability. We found that, in the mass range of 10^4 -10^5 M_{sun}, our DSs are hotter by a factor of 1.5 than those in Freese et al.(2010), are smaller in radius by a factor of 0.6, denser by a factor of 3 - 4, and more luminous by a factor of 2. Our models also confirm previous results, according to which supermassive DSs are very well approximated by (n=3)-polytropes. We also perform a first study of dark star pulsations. Our DS models have pulsation modes with timescales ranging from less than a day to more than two years in their rest frames, at z ~ 15, depending on DM particle mass and overtone number. Such pulsations may someday be used to identify bright, cool objects uniquely as DSs; if properly calibrated, they might, in principle, also supply novel standard candles for cosmological studies., Comment: 17 pages; 11 figures; revised version; accepted by ApJ

We investigate analytically the thermodynamical stability of vortices in the ground state of rotating 2-dimensional Bose-Einstein condensates confined in asymptotically homogeneous trapping potentials in the Thomas-Fermi regime. Our starting point is the Gross-Pitaevskii energy functional in the rotating frame. By estimating lower and upper bounds for this energy, we show that the leading order in energy and density can be described by the corresponding Thomas-Fermi quantities and we derive the next order contributions due to vortices. As an application, we consider a general potential of the form V(x,y) = (x^2+lambda^2 y^2)^{s/2} with slope s \in [2,infinity) and anisotropy lambda \in (0,1] which includes the harmonic (s=2) and 'flat' (s -> infinity) trap, respectively. For this potential, we derive the critical angular velocities for the existence of vortices and show that all vortices are singly-quantized. Moreover, we derive relations which determine the distribution of the vortices in the condensate i.e. the vortex pattern., Comment: Preprint of an article which was published in Physica A in 2008; 34 pages

The nature of the cosmological dark matter remains elusive. Recent studies have advocated the possibility that dark matter could be composed of ultra-light, self-interacting bosons, forming a Bose-Einstein condensate in the very early Universe. We consider models which are charged under a global U(1)-symmetry such that the dark matter number is conserved. It can then be described as a classical complex scalar field which evolves in an expanding Universe. We present a brief review on the bounds on the model parameters from cosmological and galactic observations, along with the properties of galactic halos which result from such a dark matter candidate., Comment: 17 pages; Minor corrections to reflect the published version

(Abridged) Despite the success of Cold Dark Matter (CDM) in explaining a wide range of observations, the microscopic nature of dark matter is still unknown. Attempts to detect WIMPs, the most commonly studied form, have not yet succeeded. Some predictions are even in apparent conflict with observations (e.g. cuspy-cored halos and `missing satellite problem'). Therefore, it is important to consider different forms of CDM. We focus on dark matter comprised of ultralight bosons that form a Bose-Einstein Condensate (BEC), described by a complex scalar field, and solve the Klein-Gordon and Einstein field equations to evolve the Friedmann-Robertson-Walker universe. We find, in addition to phases of radiation-, matter- and \Lambda-domination, an earlier phase of scalar-field-domination. Moreover, while WIMP CDM is non-relativistic at all times after it decouples, BEC scalar field dark matter (SFDM) is relativistic at early times, evolving from stiff to radiation-like, before it becomes non-relativistic (CDM-like) at late times. The timing of transitions between these phases yields fundamental constraints on SFDM model parameters, particle mass m and self-interaction coupling strength \lambda. We derive the range of particle parameters required to match observations of the evolving background universe, including the CMB and abundances of light elements produced by BBN, characterized by N_eff, the effective number of neutrino species, and the epoch of matter-radiation equality z_eq. This yields m >= 2.4*10^{-21} eV/c^2 and 9.5*10^{-19} eV^{-1}cm^3 <= \lambda/(mc^2)^2 <= 4*10^{-17} eV^{-1}cm^3. Our model accommodates current observations in which N_eff at BBN is higher than at z_eq, as probed by the CMB, otherwise unexplained by WIMP CDM. SFDM without self-interaction (`Fuzzy Dark Matter') cannot satisfy current BBN constraints within 68% confidence and is therefore disfavored., Comment: 21 pages, 6 figures, minor updates to accord with the published version in Phys. Rev. D

If cosmological cold dark matter (CDM) consists of light enough bosonic particles that their phase-space density exceeds unity, they will comprise a Bose-Einstein condensate (BEC). The nature of this BEC-CDM as a quantum fluid may then distinguish it dynamically from the standard form of CDM involving a collisionless gas of non-relativistic particles that interact purely gravitationally. We summarize some of the dynamical properties of BEC-CDM that may lead to observable signatures in galactic halos and present some of the bounds on particle mass and self-interaction coupling strength that result from a comparison with observed galaxies., Comment: 10 pages, 5 figures; Minor corrections to reflect the published version

(Abridged) Extensions of the standard model of particle physics predict very light bosons, ranging from about 10^{-5} eV for the QCD axion to 10^{-33} eV for ultra-light particles, which could be the cold dark matter (CDM) in the Universe. If so, their phase-space density must be high enough to form a Bose-Einstein condensate (BEC). The fluid-like nature of BEC-CDM dynamics differs from that of standard collisionless CDM (sCDM), so observations of galactic haloes may distinguish them. sCDM has problems with galaxy observations on small scales, which BEC-CDM may overcome for a large range of particle mass m and self-interaction strength g. For quantum-coherence on galactic scales of radius R and mass M, either the de-Broglie wavelength lambda_deB <~ R, requiring m >~ m_H \cong 10^{-25}(R/100 kpc)^{-1/2}(M/10^{12} M_solar)^{-1/2} eV, or else lambda_deB << R but self-interaction balances gravity, requiring m >> m_H and g >> g_H \cong 2 x 10^{-64} (R/100 kpc)(M/10^{12} M_solar)^{-1} eV cm^3. Here we study the largely-neglected effects of angular momentum. Spin parameters lambda \cong 0.05 are expected from tidal-torquing by large-scale structure, just as for sCDM. Since lab BECs develop quantum vortices if rotated rapidly enough, we ask if this angular momentum is sufficient to form vortices in BEC haloes, affecting their structure with potentially observable consequences. The minimum angular momentum for this, L_{QM} = $\hbar M/m$, requires m >= 9.5 m_H for lambda = 0.05, close to the particle mass required to influence structure on galactic scales. We study the equilibrium of self-gravitating, rotating BEC haloes which satisfy the Gross-Pitaevskii-Poisson equations, to calculate if and when vortices are energetically favoured. Vortices form as long as self-interaction is strong enough, which includes a large part of the range of m and g of interest for BEC-CDM haloes., Comment: Several typos and numerical typos (incl. in Fig.6, Table 2 and Table 3) have been corrected and references have been updated after proof-reading stage; MNRAS in press; 29 pages; 11 figures

If cold dark matter elementary particles form a Bose-Einstein condensate, their superfluidity may distinguish them from other forms of cold dark matter, including creation of quantum vortices. We demonstrate here that such vortices are favoured in strongly-coupled condensates, while this is not the case for axions, which are generally presumed to form a Bose-Einstein condensate but are effectively non-interacting., Comment: 5 pages, 1 figure; minor corrections; final version, to appear in 'New Horizons in Astronomy (Bash Symposium 2009)', Proceedings of the Astronomical Society of the Pacific, eds. L. Stanford, L. Hao, Y. Mao, J. Green