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Register a new userCosmological perturbations for ultra-light axion-like particles in a state of Bose-Einstein condensate
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Authors
Shinji Tsujikawa
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For ultra-light scalar particles like axions, dark matter can form a state of the Bose-Einstein condensate (BEC) with a coherent classical wave whose wavelength is of order galactic scales. In the context of an oscillating scalar field with mass $m$, this BEC description amounts to integrating out the field oscillations over the Hubble time scale $H^{-1}$ in the regime $m gg H$. We provide a gauge-invariant general relativistic framework for studying cosmological perturbations in the presence of a self-interacting BEC associated with a complex scalar field. In particular, we explicitly show the difference of BECs from perfect fluids by taking into account cold dark matter, baryons, and radiation as a Schutz-Sorkin description of perfect fluids. We also scrutinize the accuracy of commonly used Newtonian treatment based on a quasi-static approximation for perturbations deep inside the Hubble radius. For a scalar field which starts to oscillate after matter-radiation equality, we show that, after the BEC formation, a negative self-coupling hardly leads to a Laplacian instability of the BEC density contrast. This is attributed to the fact that the Laplacian instability does not overwhelm the gravitational instability for self-interactions within the validity of the nonrelativistic BEC description. Our analysis does not accommodate the regime of parametric resonance which can potentially occur for a large field alignment during the transient epoch prior to the BEC formation.
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Light scalars (as the axion) with mass m ~ 10^{-22} eV forming a Bose-Einstein condensate (BEC) exhibit a Jeans length in the kpc scale and were therefore proposed as dark matter (DM) candidates. Our treatment here is generic, independent of the particle physics model and applies to all DM BEC, in or out of equilibrium. Two observed quantities crucially constrain DM in an inescapable way: the average DM density rho_{DM} and the phase-space density Q. The observed values of rho_{DM} and Q in galaxies today constrain both the possibility to form a BEC and the DM mass m. These two constraints robustly exclude axion DM that decouples just after the QCD phase transition. Moreover, the value m ~ 10^{-22} eV can only be obtained with a number of ultrarelativistic degrees of freedom at decoupling in the trillions which is impossible for decoupling in the radiation dominated era. In addition, we find for the axion vacuum misalignment scenario that axions are produced strongly out of thermal equilibrium and that the axion mass in such scenario turns to be 17 orders of magnitude too large to reproduce the observed galactic structures. Moreover, we also consider inhomogenous gravitationally bounded BECs supported by the bosonic quantum pressure independently of any particular particle physics scenario. For a typical size R ~ kpc and compact object masses M ~ 10^7 Msun they remarkably lead to the same particle mass m ~ 10^{-22} eV as the BEC free-streaming length. However, the phase-space density for the gravitationally bounded BECs turns to be more than sixty orders of magnitude smaller than the galaxy observed values. We conclude that the BECs and the axion cannot be the DM particle. However, an axion in the mili-eV scale may be a relevant source of dark energy through the zero point cosmological quantum fluctuations.
Cosmological observations are used to test for imprints of an ultra-light axion-like field (ULA), with a range of potentials $V(phi)propto[1-cos(phi/f)]^n$ set by the axion-field value $phi$ and decay constant $f$. Scalar field dynamics dictate that the field is initially frozen and then begins to oscillate around its minimum when the Hubble parameter drops below some critical value. For $n!=!1$, once dynamical, the axion energy density dilutes as matter; for $n!=!2$ it dilutes as radiation and for $n!=!3$ it dilutes faster than radiation. Both the homogeneous evolution of the ULA and the dynamics of its linear perturbations are included, using an effective fluid approximation generalized from the usual $n=1$ case. ULA models are parameterized by the redshift $z_c$ when the field becomes dynamical, the fractional energy density $f_{z_c} equiv Omega_a(z_c)/Omega_{rm tot}(z_c)$ in the axion field at $z_c$, and the effective sound speed $c_s^2$. Using Planck, BAO and JLA data, constraints on $f_{z_c}$ are obtained. ULAs are degenerate with dark energy for all three potentials if $1+z_c lesssim 10$. When $3times10^4 gtrsim 1+z_c gtrsim 10 $, $f_{z_c}$ is constrained to be $ lesssim 0.004 $ for $n=1$ and $f_{z_c} lesssim 0.02 $ for the other two potentials. The constraints then relax with increasing $z_c$. These results strongly constrain ULAs as a resolution to cosmological tensions, such as discrepant measurements of the Hubble constant, or the EDGES measurement of the global 21 cm signal.
We calculate the production of ultra-light axion-like particles (ALPs) in a nearby supernova progenitor. Once produced, ALPs escape from the star and a part of them is converted into photons during propagation in the Galactic magnetic field. It is found that the MeV photon flux that reaches Earth may be detectable by gamma ray telescopes for ALPs lighter than ~1 neV when Betelgeuse undergoes oxygen and silicon burning. (Non-)detection of gamma rays from a supernova progenitor with next-generation gamma ray telescopes just after pre-supernova neutrino alerts would lead to an independent constraint on ALP parameters as stringent as a SN 1987A limit.
Ultra-light axion-like particle (ULAP) is one of attractive candidates for cold dark matter. Because the de Broglie wavelength of ULAP with mass $sim 10^{-22} {rm eV}$ is $mathcal{O}({rm kpc})$, the suppression of the small scale structure by the uncertainty principle can solve the core-cusp problem. Frequently, ULAP is assumed to be uniformly distributed in the present universe. In typical ULAP potentials, however, strong self-resonance at the beginning of oscillation invokes the large fluctuations, which may cause the formation of the dense localized object, oscillon. % Such a dense object lives for a long time, it may affect the cosmological evolution. In this paper, we confirm the oscillon formation in a ULAP potential by numerical simulation and analytically derive its lifetime.
The fact that fast oscillating homogeneous scalar fields behave as perfect fluids in average and their intrinsic isotropy have made these models very fruitful in cosmology. In this work we will analyse the perturbations dynamics in these theories assuming general power law potentials $V(phi)=lambda vertphivert^{n}/n$. At leading order in the wavenumber expansion, a simple expression for the effective sound speed of perturbations is obtained $c_{text{eff}}^2 = omega=(n-2)/(n+2)$ with $omega$ the effective equation of state. We also obtain the first order correction in $k^2/omega_{text{eff}}^2$, when the wavenumber $k$ of the perturbations is much smaller than the background oscillation frequency, $omega_{text{eff}}$. For the standard massive case we have also analysed general anharmonic contributions to the effective sound speed. These results are reached through a perturbed version of the generalized virial theorem and also studying the exact system both in the super-Hubble limit, deriving the natural ansatz for $deltaphi$; and for sub-Hubble modes, exploiting Floquets theorem.
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