Axions and axion-like particles are compelling candidates for the missing dark matter of the universe. As they undergo gravitational collapse, they can form compact objects such as axion stars or even black holes. In this paper, we study the formation and distribution of such objects. First, we simulate the formation of compact axion stars using numerical relativity with aspherical initial conditions that could represent the final stages of axion dark matter structure formation. We show that the final states of such collapse closely follow the known relationship of initial mass and axion decay constant $f_a$. Second, we demonstrate with a toy model how this information can be used to scan a model density field to predict the number densities and masses of such compact objects. In addition to being detectable by the LIGO/VIRGO gravitational wave interferometer network for axion mass of $10^{-9} < m_a < 10^{-11}$ eV, we show using peak statistics that for $f_a < 0.2M_{pl}$, there exists a "mass gap" between the masses of axion stars and black holes formed from collapse.
The number of nonrelativistic axions can be changed by inelastic reactions that produce photons or relativistic axions. Any odd number of axions can annihilate into two photons. Any even number of nonrelativistic axions can scatter into two relativistic axions. We calculate the rate at which axions are lost from axion stars from these inelastic reactions. In dilute systems of axions, the dominant inelastic reaction is axion decay into two photons. In sufficiently dense systems of axions, the dominant inelastic reaction is the scattering of four nonrelativistic axions into two relativistic axio…
We investigate aspects of axion as a coherently oscillating massive classical scalar field by analyzing third order perturbations in Einstein's gravity in the axion-comoving gauge. The axion fluid has its characteristic pressure term leading to an axion Jeans scale which is cosmologically negligible for a canonical axion mass. Our classically derived axion pressure term in Einstein's gravity is identical to the one derived in the non-relativistic quantum mechanical context in the literature. We show that except for the axion pressure term, the axion fluid equations are exactly the same as the …
We study the gravitational collapse of an axion field in null coordinates, assuming spherical symmetry. Compared with previous studies, we use a simpler numerical scheme which can run, for relevant parameters, in a few minutes or less on a desktop computer. We use it to accurately determine the domains of parameter space in which the axion field forms a black hole, an axion star or a relativistic Bosenova.
The QCD axion acquires the potential through the non-perturbative effect of the QCD matters around the QCD phase transition. During this period, the direct interaction between the axion and the QCD matters sets in. Focusing on the impact of this direct interaction, we propose two scenarios where the fluctuation of the axion can rapidly grow, potentially leading to the formation of axion miniclusters even if the Peccei-Quinn (PQ) symmetry was already broken during inflation. The first scenario assumes that the primordial curvature perturbation at the horizon scale during the QCD epoch was signi…
Emission of relativistic axions from transient sources, such as axion star explosions, can lead to observable signatures. We show that axion bursts from collapsing axion stars can be detectable over the wide range of axion masses $10^{-15} \, \textrm{eV} \lesssim m \lesssim 10^{-7} \, \textrm{eV}$ in laboratory experiments, such as ABRACADABRA, DMRadio and SHAFT. The detection of axion bursts could provide new insights into the fundamental axion potential, which is challenging to probe otherwise. An ensemble of bursts in the distant past would give rise to a diffuse axion background distinct f…
We consider cosmological applications of a new self-consistent system of equations, accounting for a nonminimal coupling of the gravitational, electromagnetic and pseudoscalar (axion) fields in a relativistic plasma. We focus on dispersion relations for electromagnetic perturbations in an initially isotropic ultrarelativistic plasma coupled to the gravitational and axion fields in the framework of isotropic homogeneous cosmological model of the de Sitter type. We classify the longitudinal and transversal electromagnetic modes in an axionically active plasma and distinguish between waves (dampi…
The QCD axion and an axion-like particle (ALP) are compelling candidates of dark matter. For the QCD axion, it is known that when the Peccei-Quinn (PQ) symmetry is spontaneously broken after inflation, the large initial fluctuation can lead to axion clump formation. On the other hand, when the symmetry is already broken during inflation, it has been believed that the axion clump formation does not occur due to the small amplitude of the initial axion fluctuation. We revisit this prevailing understanding, considering both the QCD axion and an ALP. We find that for the QCD axion, the clump forma…
Rice University（莱斯大学）；Black Hole Initiative at Harvard University（哈佛黑洞倡议项目）；Harvard-Smithsonian Center for Astrophysics（哈佛-史密森尼天体物理中心）；University of Texas at San Antonio（德克萨斯大学圣安东尼奥分校）
The substructures of light bosonic (axion-like) dark matter may condense into compact Bose stars. We study collapses of the critical-mass stars caused by attractive self-interaction of the axion-like particles and find that these processes proceed in an unexpected universal way. First, nonlinear self-similar evolution (called "wave collapse" in condensed matter physics) forces the particles to fall into the star center. Second, interactions in the dense center create an outgoing stream of mildly relativistic particles which carries away an essential part of the star mass. The collapse stops wh…
We derive oscillating gravitational potential caused by an ultralight axion as the cosmic dark matter, assuming the Compton wavelength smaller than the horizon scale. A new oscillatory term is found which dominates the previously known one on scales larger than the quantum Jeans-scale. In the context of linear perturbations in cosmology this new term might be more relevant in future observation. Both the quantum stress in density perturbation and the quantum oscillation of the gravitational potential are derived in the zero-shear gauge. We show that the axion fluid in relativistic analysis is …
Axion as a coherently oscillating massive scalar field is known to behave as a zero-pressure irrotational fluid with characteristic quantum stress on a small scale. In relativistic perturbation theory, the case was proved in the axion-comoving gauge up to fully nonlinear and exact order. Our basic assumption is that the field is oscillating with Compton frequency and the Compton wavelength is smaller than the horizon scale. Here, we revisit the relativistic proof to the linear order in the other gauge conditions. We show that the same equation for density perturbation known in the non-relativi…
Axions are some of the best motivated particles beyond the Standard Model. We show how the attractive self-interactions of dark matter (DM) axions over a broad range of masses, from $10^{-22}$ eV to $10^7$ GeV, can lead to nongravitational growth of density fluctuations and the formation of bound objects. This structure formation enhancement is driven by parametric resonance when the initial field misalignment is large, and it affects axion density perturbations on length scales of order the Hubble horizon when the axion field starts oscillating, deep inside the radiation-dominated era. This e…
The Peccei-Quinn mechanism presents a neat solution to the strong CP problem. As a by-product, it provides an ideal dark matter candidate, "the axion", albeit with a tiny mass. Axions therefore can act as dark radiation if excited with large momenta after the end of inflation. Nevertheless, the recent measurement of relativistic degrees of freedom from cosmic microwave background radiation strictly constrains the abundance of such extra relativistic species. We show that ultra-relativistic axions can be abundantly produced if the Peccei-Quinn field was initially displaced from the minimum of t…
Taking a comprehensive view, including a full range of boundary conditions, we reexamine QCD axion star solutions based on the relativistic Klein-Gordon equation (using the Ruffini-Bonazzola approach) and its non-relativistic limit, the Gross-Pitaevskii equation. A single free parameter, conveniently chosen as the central value of the wavefunction of the axion star, or alternatively the chemical potential with range $-m<μ< 0$ (where $m$ is the axion mass), uniquely determines a spherically-symmetric ground state solution, the axion condensate. We clarify how the interplay of various terms of t…
If axion-like particles (ALPs) constitute a major part of dark matter (DM), due to the bosonic nature and a relative small mass, they could behave differently from the point like dark matter particles on the formation of the cosmic structures. When studying the structure formation, it is often useful to consider DM as a special fluid with a given density and a given velocity. ALP fluid obeys a same continuity equation comparing to the point-like collisionless DM but has a different first-order velocity equation. In the linear regime of structure formation, the resulted observational difference…
The classical equations of motion for an axion with potential $V(ϕ)=m_a^2f_a^2 [1-\cos (ϕ/f_a)]$ possess quasi-stable, localized, oscillating solutions, which we refer to as "axion stars". We study, for the first time, collapse of axion stars numerically using the full non-linear Einstein equations of general relativity and the full non-perturbative cosine potential. We map regions on an "axion star stability diagram", parameterized by the initial ADM mass, $M_{\rm ADM}$, and axion decay constant, $f_a$. We identify three regions of the parameter space: i) long-lived oscillating axion star sol…
We point out that domain wall formation is a more common phenomenon in the Axiverse than previously thought. Level crossing could take place if there is a mixing between axions, and if some of the axions acquire a non-zero mass through non-perturbative effects as the corresponding gauge interactions become strong. The axion potential changes significantly during the level crossing, which affects the axion dynamics in various ways. We find that, if there is a mild hierarchy in the decay constants, the axion starts to run along the valley of the potential, passing through many crests and troughs…
Existing searches for cosmic axions relics have relied heavily on the axion being non-relativistic and making up dark matter. However, light axions can be copiously produced in the early Universe and remain relativistic today, thereby constituting a Cosmic $\textit{axion}$ Background (C$a$B). As prototypical examples of axion sources, we consider thermal production, dark-matter decay, parametric resonance, and topological defect decay. Each of these has a characteristic frequency spectrum that can be searched for in axion direct detection experiments. We focus on the axion-photon coupling and …
The coherent oscillation of axionic fields naturally drives copious production of dark photon particles in the early universe, due to resonance and tachyonic enhancement. During the process, energy is abruptly transferred from the former to the latter, sourcing gravitational wave generation. The resulting gravitational waves are eventually to be observed as stochastic background today. We report analytical results of this production and connect them to the recent pulsar-timing results by the NANOGrav collaboration. We show an available parameter space, around the mass $m_ϕ\sim 10^{-13} \, {\rm…
We consider a general class of axion models, including the QCD and string axion, in which the PQ symmetry is broken before or during inflation. Assuming the axion is the dominant component of the dark matter, we discuss axion star formation in virialized dark minihalos around primordial black holes through gravitational Bose-Einstein condensation. We determine the conditions for minihalos to kinetically produce axion stars before galaxy formation. Today, we expect up to $\sim 10^{17}$ ($\sim 10^9$) axion stars in a radius of 100 parsecs around the Sun for the case of the QCD (string) axion.
Axions as dark matter is an increasingly important subject in astrophysics and cosmology. Experimental and observational searches are mounting across the mass spectrum of axion-like particles, many of which require detailed knowledge of axion structure over a wide range of scales. Current understanding of axion structures is far from complete, however, due largely to controversy in modeling the candidate's highly-degenerate state. The series Axion Structure Formation seeks to develop a consistent model of QCD axion dark matter dynamics that follows their highly-degenerate nature to the present…
Axion stars are hypothetical objects formed of axions, obtained as localized and coherently oscillating solutions to their classical equation of motion. Depending on the value of the field amplitude at the core $|θ_0| \equiv |θ(r=0)|$, the equilibrium of the system arises from the balance of the kinetic pressure and either self-gravity or axion self-interactions. Starting from a general relativistic framework, we obtain the set of equations describing the configuration of the axion star, which we solve as a function of $|θ_0|$. For small $|θ_0| \lesssim 1$, we reproduce results previously obta…
We revisit the model of axion inflation in the context of stochastic inflation and investigate the effects of the stochastic noises associated to the electromagnetic fields. Because of the parity violating interaction, one polarization of the gauge field is amplified inducing large curvature perturbation power spectrum. Taking into account the stochastic kicks arising from the short modes at the time of horizon crossing we obtain the corresponding Langevin equations for the long modes of the electromagnetic and axion fields. It is shown that a mean-reverting process governs the dynamics of the…
Lattice study of primordial black hole formation in bumpy axion inflation
Kavli IPMU (WPI), UTIAS, University of Tokyo（东京大学）；ICRR, University of Tokyo（东京大学）；Physics Division, Faculty of Science, Kanagawa University（神奈川大学）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), RIKEN（理化学研究所）；Department of Physics, Tohoku University（东北大学）
In the axion monodromy inflation, the inflation is driven by the axion with super-Planckian field values in a monomial potential with superimposed sinusoidal modulations. The coupling of the axion to massless gauge fields can induce copious particle production during inflation, resulting in large non-Gaussian curvature perturbation that leads to the formation of primordial black holes. In this paper, we explore the parameter space in the axion monodromy inflation model that favors the formation of primordial black holes with masses ranging from $10^8$ grams to $20$ solar masses. We also study …
We study the formation and the subsequent mass growth of axion stars inside axion miniclusters. Numerically solving the Schrödinger-Poisson equations with realistic initial conditions we find that the axion stars exhibit similar properties to solitonic cores in ultralight bosonic dark matter halos in terms of their radial density profiles and large-amplitude oscillations. A merger of two axion stars confirms a previously found empirical law for the mass of the merged axion star. Monitoring the axion star masses over time, we observe a mass growth consistent with the mass increase of Bose stars…
The first paper in this series showed that QCD axion dark matter, as a highly-correlated Bose fluid, contains extra-classical physics on cosmological scales. The nature of the derived extra-classical physics is exchange-correlation interactions induced by the constraints of symmetric particle exchange and inter-axion correlations from self-gravitation. The paper also showed that the impact of extra-classical physics on early structure formation is marginal, as the exchange-correlation interaction is inherently non-linear. This paper continues the study of axion structure formation into the non…
Coherent oscillation of axions or axion-like particles may give rise to long-lived clumps, called axion stars, because of the attractive gravitational force or its self-interaction. Such a kind of configuration has been extensively studied in the context of oscillons without the effect of gravity, and its stability can be understood by an approximate conservation of particle number in a non-relativistic effective field theory (EFT). We extend this analysis to the case with gravity to discuss the longevity of axion stars and clarify the EFT expansion scheme in terms of gradient energy and Newto…
We study the future prospects of the 21cm forest observations on the axion-like dark matter when the spontaneous breaking of the global Peccei-Quinn (PQ) symmetry occurs after the inflation. The large isocurvature perturbations of order unity sourced from axion-like particles can result in the enhancement of minihalo formation, and the subsequent hierarchical structure formation can affect the minihalo abundance whose masses can exceed ${\cal O}(10^4) M_{\odot}$ relevant for the 21cm forest observations. We show that the 21cm forest observations are capable of probing the axion-like particle m…
We investigate the structure of gravitational self-interactions of coherently oscillating axions in the general relativistic framework. A generic action for a massive scalar field in the Friedmann-Robertson-Walker background is first introduced based on the effective field theory approach to cosmological perturbations. Using the obtained setup, we evaluate the effective gravitational interaction of the massive scalar field, i.e. scalar quartic interactions mediated by metric perturbations. Applying the results to the system of dark matter axions, we estimate their self-interaction rate and dis…
Primordial electromagnetic fields can strongly affect the cosmic evolution of axions, and vice versa. We show that if helical electromagnetic fields are coherently produced in the early universe, their remnants source a field velocity to the coupled axions and enhance the relic abundance of axion dark matter. We discuss the implications for the QCD axion and axion-like particles that are coupled to the SM or hidden gauge groups. For a QCD axion coupled to hidden photons, we find that the conventional window for the axion decay constant $10^{8}\, \mathrm{GeV} \lesssim f \lesssim 10^{12}\, \math…
We argue that the existence of the cold dark matter is explained by primordial black holes.We show that a significant number of primordial black holes can be formed in an axion-like curvaton model, in which the highly blue-tilted power spectrum of primordial curvature perturbations is achieved.It is found that the produced black holes with masses $\sim 10^{20} -10^{38} \mathrm{g}$ account for the present cold dark matter.We also argue the possibility of forming the primordial black holes with mass $\sim 10^5 M_{\odot}$ as seeds of the supermassive black holes.
We derive structure formation limits on dark matter (DM) composed of keV-scale axion-like particles (ALPs), produced via freeze-in through the interactions with photons and Standard Model (SM) fermions. We employ Lyman-alpha (Ly-α) forest data sets as well as the observed number of Milky Way (MW) subhalos. We compare results obtained using Maxwell-Boltzmann and quantum statistics for describing the SM bath. It should be emphasized that the presence of logarithmic divergences complicates the calculation of the production rate, which can not be parameterized with a simple power law behaviour. Th…
We present a scenario that ameliorates the tuning problems present in models of primordial black hole dark matter from inflation. Our setup employs the advantages of gravitational collapse in a long epoch of early matter domination with reheating temperature $\lesssim 10^{6}~\text{GeV}$. Furthermore, we make use of a string-inspired class of models where the inflaton is identified with a non-compact axion field. In this framework, the presence of multiple local minima in the inflaton potential can be traced back to an approximate discrete shift symmetry. This scenario allows the formation of p…
If the symmetry breaking responsible for axion dark matter production occurs during the radiation-dominated epoch in the early Universe, then this produces large amplitude perturbations that collapse into dense objects known as axion miniclusters. The characteristic minicluster mass, $M_0$, is set by the mass inside the horizon when axion oscillations begin. For the QCD axion $M_0\sim 10^{-10}M_\odot$, however for an axion-like particle $M_0$ can approach $M_\odot$ or higher. Using the Press-Schechter formalism we compute the mass function of halos formed by hierarchical structure formation fr…
In this article, we study the implications of the coupling between Axion-Like-Particles (ALPs) and Leptons to cosmology, in particular, the Big Bang Nucleosynthesis (BBN). We show that the BBN, through the constraint on the effective number of relativistic neutrino species, provides the most stringent bound on the ALP-electron interaction strength for the mass of axion between 20 keV and 1 MeV. For other values of the mass, the BBN bound complements the stellar-evolution and laboratory bounds.
If the symmetry breaking inducing the axion occurs after the inflation, the large axion isocurvature perturbations can arise due to a different axion amplitude in each causally disconnected patch. This causes the enhancement of the small-scale density fluctuations which can significantly affect the evolution of structure formation. The epoch of the small halo formation becomes earlier and we estimate the abundance of those minihalos which can host the neutral hydrogen atoms to result in the 21cm fluctuation signals. We find that the future radio telescopes, such as the SKA, can put the axion m…
Axion stars, gravitationally bound states of low-energy axion particles, have a maximum mass allowed by gravitational stability. Weakly bound states obtaining this maximum mass have sufficiently large radii such that they are dilute, and as a result, they are well described by a leading-order expansion of the axion potential. Heavier states are susceptible to gravitational collapse. Inclusion of higher-order interactions, present in the full potential, can give qualitatively different results in the analysis of collapsing heavy states, as compared to the leading-order expansion. In this work, …
The string/$M$ theory Axiverse -- a plethora of very light Axion Like Particles (ALPs) with a vast range of masses -- is arguably a generic prediction of string/$M$ theory. String/$M$ theory also tends to predict that the early Universe is dominated by moduli fields. When the heavy moduli decay, before nucleosynthesis, they produce dark radiation in the form of relativistic ALPs. Generically one estimates that the number of relativistic species grows with the number of axions in the Axiverse, in contradiction to the observations that $N_{eff} \leq 4$. We explain this problem in detail and sugg…
There are several issues to do with dwarf galaxy predictions in the standard $Λ$CDM cosmology that have suscitated much recent debate about the possible modification of the nature of dark matter as providing a solution. We explore a novel solution involving ultra-light axions that can potentially resolve the missing satellites problem, the cusp-core problem, and the `too big to fail' problem. We discuss approximations to non-linear structure formation in dark matter models containing a component of ultra-light axions across four orders of magnitude in mass, $10^{-24}\text{ eV}\lesssim m_a \les…
We investigate cosmological structure formation in Fuzzy Dark Matter (FDM) with an attractive self-interaction (SI) with numerical simulations. Such a SI would arise if the FDM boson were an ultra-light axion, which has a strong CP symmetry-breaking scale (decay constant). Although weak, the attractive SI may be strong enough to counteract the quantum 'pressure' and alter structure formation. We find in our simulations that the SI can enhance small-scale structure formation, and soliton cores above a critical mass undergo a phase transition, transforming from dilute to dense solitons.
We prove that the axion as a coherently oscillating scalar field acts as a cold dark matter (CDM) to the second-order perturbations in all cosmological scales including the super-horizon scale. The proof is made in the axion-comoving gauge. For a canonical mass, the axion pressure term causes deviation from the CDM only on scales smaller than the Solar System size. Beyond such a small scale the equations of the axion fluid are the same as the ones of the CDM based on the CDM-comoving gauge which are exactly identical to the Newtonian equations to the second order. We also show that the axion f…
Relativistic axions are good candidates for the dark radiation for which there are mounting observational hints. The primordial decays of heavy fields produce axions which are ultra-energetic compared to thermalised matter and inelastic axion-matter scattering can occur with $E_{CoM} \gg T_γ$, thus accessing many interesting processes which are otherwise kinematically forbidden in standard cosmology. Axion-photon scattering into quarks and leptons during BBN affects the light element abundances, and bounds on overproduction of $^4$He constrain a combination of the axion decay constant and the …
The non-linear hydrodynamic equations for axion/scalar field dark matter (DM) in the non-relativistic Madelung-Shcrödinger form are derived in a simple manner, including the effects of universal expansion and Hubble drag. The hydrodynamic equations are used to investigate the relative velocity between axion DM and baryons, and the moving-background perturbation theory (MBPT) derived. Axions massive enough to be all of the DM do not affect the coherence length of the relative velocity, but the MBPT equations are modified by the inclusion of the axion effective sound speed. These MBPT equations …
Non-relativistic QCD axions or axion-like particles are among the most popular candidates for cold Dark Matter (DM) in the universe. We proposed to detect axion-like DM, using linearly polarized pulsar light as a probe. Because of birefringence effect potentially caused by an oscillating galactic axion DM background, when pulsar light travels across the galaxy, its linear polarization angle may vary with time. With a soliton+NFW galactic DM density profile, we show that this strategy can potentially probe an axion-photon coupling as small as $\sim 10^{-13}$ GeV$^{-1}$ for axion mass $m_a \sim …
We analyze the spectrum of axions radiated from collapse of domain walls, which have received less attention in the literature. The evolution of topological defects related to the axion models is investigated by performing field-theoretic lattice simulations. We simulate the whole process of evolution of the defects, including the formation of global strings, the formation of domain walls and the annihilation of the defects due to the tension of walls. The spectrum of radiated axions has a peak at the low frequency, which implies that axions produced by the collapse of domain walls are not hig…
Axions in the Peccei-Quinn (PQ) mechanism provide a promising solution to the strong CP problem in the standard model of particle physics. Coherently generated PQ scalar fields could dominate the energy density in the early Universe and decay into relativistic axions, which would conflict with the current dark radiation constraints. We study the possibility that a thermal inflation driven by a $U(1)$ gauged Higgs field dilutes such axions. A well-motivated extra gauged $U(1)$ would be the local $B-L$ symmetry. We also discuss the implication for the case of $U(1)_{B-L}$ and an available baryog…
We study the formation of primordial black holes (PBHs) from the collapse of closed domain walls (DWs) which naturally arise in QCD axion models near the QCD scale together with the main string-wall network. The size distribution of the closed DWs is determined by percolation theory, from which we further obtain PBH mass distribution and abundance. Various observational constraints on PBH abundance in turn also constrain axion parameters. Our model prefers axion mass around the meV scale ($f_{a}\sim 10^{9}$ GeV). The corresponding PBHs are in the sublunar-mass window $10^{20}$-$10^{22}$ g (i.e…
Extending the Standard Model with a new complex singlet scalar, right-handed neutrinos and a vector-like quark allows to simultaneously tackle several problems in particle physics and cosmology within a constrained framework that can be falsified by future probes of the cosmic microwave background, as well as by upcoming axion experiments. This Standard Model - Axion - Seesaw - H portal inflation theory (SMASH) provides predictive inflation and $H$ boson stabilization, and can explain baryogenesis, light neutrino masses, dark matter and the strong CP problem. The model contains a unique new ma…
