REVIEW
Dark Matter from an ultra-light pseudo-Goldsone-boson
High Energy Physics - Phenomenology · Submitted 23 Sep 2005 · 18 references
Pith's verdict: A modest, honest 2005 paper: a compact unified free-streaming formula plus an order-of-magnitude f_I bound whose scalar kernel is asserted rather than checked.
T0 · AI review
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Referee report
The paper
The paper claims
A pseudo-Goldstone boson with a mass between the dark-energy and fuzzy-dark-matter scales would free-stream and suppress small-scale structure; the authors turn that suppression into bounds on how large a share of the dark matter it can be.
The reading
What carries the argument
The load-bearing object is the free-streaming suppression factor $r(k)$, defined as the ratio of the true density-perturbation power to what it would be without free streaming. It is built from two ingredients: the redshift at which the field starts to oscillate, fixed by $Happrox m_I$, and the Jeans-like wavenumber $k_J(a)$ at which the field's pressure balances gravity, $k_phi^J(a)=1.56,a^{1/4}m_phi^{1/2}H_0^{1/2}Omega_m^{1/4}$ for the scalar and $k_nu^J(a)=1.22,a^{1/2}m_nu T_nu^0/(H_0Omega_m^{1/2})$ for the neutrino. The ratio of the scale factor at the start of the clustering interval to that at its end, raised to $2(p-1)$ with $p$ the growth exponent of the density contrast in a mixture of matter and a smooth component, gives the suppression. The same algebra, with $f=f_nu=0.011,h^2Omega_m,m_{eV}$, reproduces the standard neutrino result, which is what makes the paper's treatment unified.
Extended reading notes
Core claim
The central claim is that current cosmological data already bound the density fraction $f_I$ of an intermediate-mass pseudo-Goldstone boson, and that the bound can be computed with a single analytic free-streaming kernel rather than a numerical Boltzmann solve for each mass. The kernel is $r(k)=(a_{max}/a_{min})^{2(p-1)}$ with $p=frac{1}{4}(sqrt{1+24(1-f)}-1)$, where $a_{min}=max(a_m,a_{eq})$ and $a_{max}=min(a_0,a_J(k))$ bracket the interval during which the field clusters. Specialising to the scalar gives $r_phi(k)approx(k_{phi,min}/k_{phi,max})^{8(1-p)}$ with $k_{phi,min}=max(k_{phi,eq},k_{phi,m})$ and $k_{phi,max}=min(k,k_{phi,0})$, and specialising to the neutrino gives $r_nu(k)approx(k_{NR}/k_{nu,max})^{4(1-p)}$. Feeding these into a likelihood over $tau$, $Omega_m h^2$, $n_s$ and $h$, with $Omega_b h^2=0.023$ fixed, the authors find that for $m_I$ between roughly $10^{-30}$ and $10^{-24}$ eV the fraction $f_I$ is limited to about 10% or less, while over the wider range $10^{-31}$ to $10^{-23}$ eV the field can be at most a sub-dominant component of the dark matter. The paper presents this as a bound with room for improvement from near-future data.
Load-bearing premise
The bounds rest on the analytic free-streaming suppression $r(k)$ being accurate at roughly the 10% level the authors claim, even though the field's switch from frozen ($w_I=-1$) to matter-like ($w_I=0$) behaviour at $a_F$ is modelled as a sharp transition and the paper itself notes that using $r(k)$ directly as a power-spectrum normalisation is in principle not precise without a numerical check.
Editorial extensions
If this is right
- For $m_I$ between about $10^{-30}$ and $10^{-24}$ eV, existing CMB, galaxy-survey, $sigma_8$ and Lyman-alpha data together cap the intermediate field's share of the dark matter at roughly 10%.
- Across the wider window $10^{-31}$ to $10^{-23}$ eV the field is allowed only as a sub-dominant dark-matter component, with the ceiling depending on mass.
- The suppression grows toward small scales, so the Lyman-alpha forest power spectrum drives the tightest part of the bound while the CMB and $sigma_8$ give weaker but independent constraints.
- A single closed-form template covers both an ultra-light scalar and a massive neutrino, so the two can be constrained with the same machinery and compared directly.
Reading between the lines
- Because the same kernel describes a sterile-like light scalar and a massive neutrino, a few-percent $f_I$ could partly mimic a neutrino mass in Lyman-alpha fits; a joint fit of $f_I$ and $sum m_nu$ would be the natural next step and is not performed here.
- Future weak-lensing and 21-cm surveys reaching $ksim 1$ to $100,h$Mpc$^{-1}$ should tighten $f_I$ well below 10% in the mass range where current data are weakest, which is the near-future sensitivity the abstract alludes to.
- Any light relic that decouples and free-streams, such as an axion-like particle, a moduli fragment, or a dark photon with a tiny mass, inherits qualitatively similar bounds, so the template is a general tool rather than a one-model result.
Original abstract
Dark Matter (DM) and Dark Energy (DE) can be both described in terms of ultra-light Pseudo-Goldstone-Bosons (PGB) with masses m_{DM} ~ 10^{-23}eV and m_{DE} <= 10^{-33}eV respectively. Following Barbieri et al, we entertain the possibility that a PGB exists with mass m_I intermediate between these two limits, giving a partial contribution to DM. We evaluate the related effects on the power spectrum of the matter density perturbations and on the cosmic microwave background and we derive the bounds on the density fraction, f_I, of this intermediate field from current data, with room for a better sensitivity on f_I in the near future. We also give a simple and unified analytic description of the free streaming effects both for an ultra-light scalar and for a massive neutrino.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
Dark Matter (DM) and Dark Energy (DE) can be both described in terms of ultra-light Pseudo-Goldstone-Bosons (PGB) with masses m_{DM} ~ 10^{-23}eV and m_{DE} <= 10^{-33}eV respectively. Following Barbieri et al, we entertain the possibility that a PGB exists with mass m_I intermediate between these two limits, giving a partial contribution to DM. We evaluate the related effects on the power spectrum of the matter density perturbations and on the cosmic microwave background and we derive the bounds on the density fraction, f_I, of this intermediate field from current data, with room for a better sensitivity on f_I in the near future. We also give a simple and unified analytic description of the free streaming effects both for an ultra-light scalar and for a massive neutrino.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Dark Matter (DM) and Dark Energy (DE) can be both described in terms of ultra-light Pseudo-Goldstone-Bosons (PGB) with masses m_{DM} ~ 10^{-23}eV and m_{DE} <= 10^{-33}eV respectively. | background 1.00 | 0.12 | 0.14 | asserted 0.80 |
| s1 | Following Barbieri et al, we entertain the possibility that a PGB exists with mass m_I intermediate between these two limits, giving a partial contribution to DM. | contribution 0.73 | 0.26 | 0.07 | hedged possibility 0.70 |
| s2 | We evaluate the related effects on the power spectrum of the matter density perturbations and on the cosmic microwave background and we derive the bounds on the density fraction, f_I, of this intermediate field from current data, with room for a better sensitivity on f_I in the near future. | contribution 0.56 | 0.96 | 0.52 | asserted 0.98 |
| s3 | We also give a simple and unified analytic description of the free streaming effects both for an ultra-light scalar and for a massive neutrino. | contribution 0.94 | 0.88 | 0.06 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
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- references and citing sentences
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- P abstract
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References
How the literature uses it
83 arXiv papers cite this in 117 sentences
Papers citing it · 70 sentences without a confident label
Contests it 1 paper
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In this paper we have applied those results to condensates of axions forming FDM, providing corrections to similar calculations which neglect the self-interaction of axions [ref] .
Decay of Ultralight Axion Condensates · Conclusions · contest 0.81
Builds on it 1 paper
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This builds upon past work, in which the effect of ULAs was treated semi-analytically [ref] .
A search for ultra-light axions using precision cosmological data · Introduction · 0.99
Uses its method or tool 2 papers
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It is thus easiest to follow Refs. [ref] and consider $m_a$ as a fixed parameter.
Ultra-light axions and the kinetic Sunyaev-Zel'dovich Effect · Forecast for ULA abundance sensitivity of pairwise-velocity spectra · 0.81
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After this time, uses the WKB approximation to adopt an effective fluid description [ref] .
Ultra-light axions and the $S_8$ tension: joint constraints from the cosmic microwave background and galaxy clustering · Axion cosmology · 0.95
Compares with it 4 papers
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The ULA models considered here have been confronted with Lyman-$α$ and galaxy luminosity data; the resulting bounds are $m_a > 10^-22 eV$ which are comparable to the constraints we obtain in this paper [ref] .
The effects of the small-scale DM power on the cosmological neutral hydrogen (\HI) distribution at high redshifts · Conclusion · 0.97
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For a linear approach to the de Sitter state (model 1a) we obtain the mass of the Brans-Dicke scalar field [equation] while for a oscillatory approach to the de Sitter state (model 2) we have the following mass at the present epoch [equation] In the model 1b the de Sitter state is represented by a saddle-type critical point and we obtain [equation] In two first cases we obtain the mass of the Brans-Dicke scalar field as [equation] which is consistent with an upper bound on the mass of a ultralight pseudo Nambu-Goldstone bosons considered in a cosmological background [ref] .
Dynamics and cosmological constraints on Brans-Dicke cosmology · Derived quantities · 0.85
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This is in contrast to the existing constraints on ULAs in Ref. [ref] , where a grid-based likelihood and analytic approximations for the power spectra were used.
A search for ultra-light axions using precision cosmological data · Sampling · 0.97
Cites it as background 38 papers
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As is well known, the presence of such a light axion can have a major impact on the growth of large-scale structure [ref] as the sound speed for scalar dark matter is scale dependent [ref] .
Addressing the Hubble and $S_8$ Tensions with a Kinetically Mixed Dark Sector · Resolving the large-scale structure tension · 0.81
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Another candidate for dark matter with novel effects on galactic scales which is also well studied in recent past is the dark matter from ultra light axion like particles (ULAs) [ref] .
The effects of the small-scale DM power on the cosmological neutral hydrogen (\HI) distribution at high redshifts · ULA dark matter · 1.00
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This type of DM has been dubbed “fuzzy DM (FDM)" [ref] and can be naturally identified with an almost massless axion, see for instance [ref] .
Fuzzy Dark Matter from Infrared Confining Dynamics · Introduction · 0.80
Discussion
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