New cosmological mass limit on thermal relic axions

Aarhus); A.Mirizzi (Bari U. & INFN; Bari & Munich; G.Raffelt (Max Planck Inst.; Max Planck Inst.); Munich); S.Hannestad (Aarhus U.

REVIEW

New cosmological mass limit on thermal relic axions

S.Hannestad (Aarhus U., Aarhus), A.Mirizzi (Bari U. & INFN, Bari & Munich, Max Planck Inst.), G.Raffelt (Max Planck Inst., Munich)

High Energy Physics - Phenomenology · Submitted 7 Apr 2005 · 47 references

Pith's verdict: A solid, honest recomputation of axion freeze-out that yields a real 1.05 eV bound and closes the hadronic axion window; the only soft spot is the model-dependence of the one-dimensional collapse, which the authors themselves flag.

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arXiv IDhep-ph/0504059 (version 1)

Pith IDTFQTRW7G, Pith's permanent record of this paper and its review

CitationAarhus), A.Mirizzi (Bari U. & INFN, Bari & Munich, G.Raffelt (Max Planck Inst., Max Planck Inst.), Munich), S.Hannestad (Aarhus U.. "New cosmological mass limit on thermal relic axions." arXiv:hep-ph/0504059 (2005). https://pith.science/paper/TFQTRW7G

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Editor's note

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Bottom line: the 1.05 eV bound is real, and the freeze-out calculation behind it is a genuine improvement rather than a repackaging of the authors' earlier 2–3 eV number. If you work on axion cosmology, this is the number to quote for hadronic models now, and it does close the window of roughly 3×10^5 to 3×10^6 GeV that supernova 1987A left open (Sec. 5). That is worth having on a different interaction channel and a different data set than the stellar and SN arguments, which is exactly the point the summary makes and I think it is right to make it. What is actually new is the rate: the full phase-space integral of Eq. (7) with the final-state stimulation factors that Chang and Choi dropped, giving A = 0.215 and the function h(mu) of Fig. 1, plus a specified hadron spectrum for g*(T) in Table 1. The chain from Eq. (4) to Eq. (8) to Eq. (9) to Eq. (12) to the likelihood is transparent, and the approximations are given with their sizes rather than buried. Note that the classifier record says no limitations are stated; that is wrong. Sec. 3.1 gives the 10–20% freeze-out error and Sec. 3.2 the few-percent g*S/g* difference. Where I would push is the one-dimensional collapse. The paper is upfront about it in Sec. 4.3 and in the abstract's 'only if the axion-pion coupling is strongly suppressed', so this is not a hidden flaw, but it never says how much suppression of C_aπ actually matters. My own reading is that the bound is less fragile than that phrasing suggests: g* only runs from about 11 to 21 over T_D = 13–145 MeV, so the abundance moves by tens of percent, not factors. A short scaling sentence would have settled it. Second, at the top of Table 2 (f_a = 3×10^7 GeV, T_D = 145 MeV) the pion-only rate sits right at the QCD transition; the paper says it ignores color deconfinement but does not mark where the contour stops being trustworthy. For the quoted bound, T_D is nearer 40–50 MeV, so this does not touch the headline, and saying so would have cost one sentence. Third, the stated 10–20% freeze-out error is never propagated into the mass limit. Minor. This is a normal, careful JCAP-level paper. Send it out.

Referee report

Significance

The result is a genuine, independent constraint on axion parameters derived from a different interaction channel (axion-pion rather than axion-photon or axion-nucleon) and a different data set (large-scale structure and CMB rather than stellar or supernova energetics), which is exactly the kind of orthogonal handle the field needs. The chain from Eq. (4) through Eq. (9) to Eq. (12) is explicit and reproducible, the rate coefficient A = 0.215 and the function h(µ) are given numerically, the freeze-out criterion is stated to be accurate at the 10-20% level in T_D, and the use of the public CMBFAST package makes the likelihood step auditable. The comparison to Σm_ν < 0.65 eV obtained with the same data and method is a useful internal calibration, and the statement that the new bound is complementary to the mass range reachable by CAST is a concrete, falsifiable claim. The paper is also candid in the body about its approximations (the g_*S/g_* difference, the neglect of color deconfinement, the model-dependence of the 1D collapse), which is a point in its favour.

Major objections (2)

[Abstract; Sec. 4.3; Fig. 7] The abstract states that for other models the constraint is 'significantly weakened only if the axion-pion coupling is strongly suppressed', but the paper never quantifies 'strongly'. Sec. 4.3 says only that for other models 'the vertical axis in Fig. 7 must be re-scaled accordingly', which leaves the reader unable to determine how much suppression of C_aπ is required before the 1.05 eV bound relaxes materially. This is a load-bearing omission because the abstract makes a claim about the generality of the result, and the rescaling is not a simple multiplicative shift: C_aπ enters the rate as C_aπ² in Eq. (9), so a suppression factor s in C_aπ shifts T_D upward and, through g_*S(T_D) in Eq. (12), changes n_a and hence the mass limit. The authors should state explicitly, e.g. as a curve or a short table, the bound on m_a as a function of C_aπ/C_aπ^hadronic over at least the range where the post-QCD pion-rate treatment remains valid, and should identify the value of C_aπ at which the bound ceases to close the hadronic axion window.
[Sec. 2, Eq. (1) and Eq. (5); Sec. 4.3, Eq. (13)] The quoted limit m_a < 1.05 eV is computed with z = 0.56 fixed, while Sec. 2 itself notes that z could lie in the range 0.3-0.7. This is not a negligible systematic: C_aπ = (1-z)/(3(1+z)) varies from about 0.18 at z = 0.3 to about 0.06 at z = 0.7, a factor of three in coupling and a factor of nine in the rate of Eq. (9). Using the sensitivity visible in Table 2, where a factor of 100 in the rate (f_a from 3 × 10^6 to 3 × 10^7 GeV) changes n_a by only about 30%, a factor of nine in the rate translates into roughly a 15% change in n_a and therefore a comparable shift in the mass limit, i.e. a range of order 0.9-1.25 eV rather than a single number. Since the paper is careful to quote the 10-20% freeze-out uncertainty, it should propagate the z uncertainty on the same footing and state the resulting spread on the 95% CL limit in Eq. (13), or justify explicitly why z = 0.56 should be treated as exact for this purpose.

Minor objections (10)

[Sec. 3.2, Table 1, Fig. 2] The hadron spectrum of Table 1 is a fixed list, and g_* enters the Hubble rate as a square root in Eq. (11), so the omission of, for example, the f_0(980) or other resonances in the relevant temperature range shifts T_D by only a few percent. It would nonetheless be useful to state the estimated sensitivity of T_D and n_a to the assumed particle list, in the same spirit as the stated 10-20% freeze-out accuracy.
[Sec. 3.3, Table 2, Fig. 7] The last row of Table 2, f_a = 3 × 10^7 GeV with T_D = 145 MeV, lies at the QCD transition scale, where the pion-only rate of Eq. (9) and the fixed hadron gas of Table 1 are not reliable; Sec. 3.2 acknowledges ignoring color deconfinement but does not mark where this invalidates the contour. The headline bound corresponds to T_D of order 40 MeV and is unaffected, but the authors should say so explicitly and indicate the f_a value beyond which Fig. 7 should not be trusted.
[Sec. 3.1, Fig. 1] Fig. 1 shows h(µ) but does not mark the range of µ = m_π/T actually probed, which from Table 2 runs from roughly 1 to 10. Indicating this interval on the figure would make clear which part of the calculated rate controls the result.
[Sec. 3.1, Eq. (8)] The prefactor 9/4 in Eq. (8) should be annotated to state explicitly that it includes the sum over the three pionic channels and any identical-particle symmetry factors, so that a reader reproducing the matrix element does not have to infer the convention.
[Sec. 3.2, Eq. (12)] The neglect of the g_*S/g_* difference is stated to be at most a few percent, but the resulting error on n_a and hence on the mass limit is not quoted. A single sentence giving the propagated number would close the loop.
[Sec. 4.1, Table 3] The bias parameter b is listed as free and marginalized, but it is not stated whether a single bias applies to both the SDSS and the Lyman-α data or whether separate nuisance parameters are used. Given that the Lyman-α data are the input that discriminates among high-g_* models, this should be made explicit.
[Sec. 4.3, Fig. 8] The Δχ² curve of Fig. 8 would be more informative with the best-fit χ², the number of data points, and the χ² at the 95% CL boundary quoted in the text, so that the reader can judge the goodness of fit rather than only the confidence interval.
[Sec. 4.3, Figs. 5-7] The caption wording 'everything to the right of the dark shaded region is excluded at the 68% CL' is ambiguous about whether the shaded band itself is the excluded region. A phrasing such as 'the shaded regions are excluded at 68% (dark) and 95% (light) CL' would remove the ambiguity.
[Sec. 2, Eq. (1)] The displayed numerical form of Eq. (1) should be checked in proof to read m_a = 6.0 eV × (10^6 GeV/f_a); the extracted text renders it as a product, which would invert the intended scaling.
[Sec. 5] The claim that the result closes the hadronic axion window depends on the upper edge of that window as taken from Refs. [17, 18]. Since the window's boundaries are themselves subject to supernova modeling uncertainties, a sentence noting that the closure holds for the quoted window but that its upper edge is model-dependent would be appropriate.

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The paper

The paper claims

Cosmological data push the thermal-relic axion below about one electronvolt, closing a window that supernova arguments left open.

The reading

The paper asks whether the same large-scale-structure argument that yields neutrino mass limits can be turned on axions that were once in thermal equilibrium in the early universe. Axions that interact with pions strongly enough stay in equilibrium until late times; after they decouple, they free-stream and smooth out small-scale density fluctuations exactly as light neutrinos do, so a hot-dark-matter component of them can be bounded by galaxy-survey and microwave-background data. The authors compute the axion freeze-out temperature from the axion-pion interaction rather than assuming it, then feed the resulting abundance and velocity distribution into a likelihood analysis of WMAP, SDSS, supernova and Lyman-$α$ data. For hadronic axions obeying the standard mass-decay-constant relation they obtain $m_a < 1.05$ eV at 95% CL, i.e. $f_a > 5.7×10^{6}$ GeV, which would close the hadronic axion window near $10^6$ GeV that survived the supernova 1987A arguments. The same machinery gives $∑ m_ν < 0.65$ eV for neutrinos, a useful calibration of how much constraining power the data set carries.

What carries the argument

The load-bearing object is the axion-pion absorption rate $⟨Γ_a⟩_T = A (C_{aπ}/(f_a f_π))^2 T^5 h(m_π/T)$ with $A = 0.215$ and $h(0)=1$, obtained by integrating the three pion channels $a+π^0 → π^+ + π^-$ and its charged partners over thermal phase space using the squared matrix element $∑|M|^2 = (9/4)(C_{aπ}/(f_a f_π))^2 (s^2+t^2+u^2-3m_π^4)$. Setting this absorption rate equal to the Hubble rate $H = [4π^3 g_*(T)/45]^{1/2} T^2/m_{Pl}$ defines the decoupling temperature, and the value of $g_*$ there fixes the relic number density through entropy conservation, $n_a = [g_{*S}({today})/g_{*S}({decoupling})] (n_γ/2)$. The resulting density and velocity distribution are then inserted into a modified CMBFAST Boltzmann code and marginalized over seven cosmological parameters with a simulated-annealing sampler, giving the exclusion contours in the $m_a$–$g_*$ and $m_a$–$f_a$ planes.

Extended reading notes

Core claim

The central claim is a new upper bound on the mass of a thermally produced axion: $m_a < 1.05$ eV at 95% CL, equivalently $f_a > 5.7×10^{6}$ GeV, for hadronic axions that obey the standard relation $m_a = 6.0$ eV $(f_a/10^{6}$ GeV$)^{-1}$ and the hadronic axion-pion coupling $C_{aπ} = (1-z)/[3(1+z)]$ with $z = 0.56$. The bound comes from structure formation, not from stellar energy loss or from a laboratory signal: an axion that was once in thermal equilibrium and decoupled while the universe was still hot behaves as hot dark matter, suppressing power on small scales. Because the axion-pion interaction is the dominant thermalization channel in the post-QCD epoch, the authors can compute the decoupling temperature as a function of $f_a$ (ranging from about 13 MeV to 145 MeV over the plotted range) and hence the present-day axion number density, which falls from roughly 74 cm$^{-3}$ to 38 cm$^{-3}$ as $f_a$ grows. That abundance, together with the free-streaming length set by the decoupling epoch, is what the cosmological data constrain. The authors state explicitly that the result closes the hadronic axion window of roughly $3×10^{5}$ GeV $≲ f_a ≲ 3×10^{6}$ GeV at generic coupling values, and they present the two-dimensional exclusion in the $m_a$–$f_a$ plane so that other axion models can be recovered by rescaling the vertical axis.

Load-bearing premise

The 1.05 eV number assumes both the standard axion mass-decay-constant relation and the specific hadronic axion-pion coupling with $z = 0.56$; if the axion-pion coupling is suppressed, the same data allow a heavier axion.

Editorial extensions

If this is right

Hadronic axions with masses of a few eV, previously tolerated in the supernova 1987A window around $f_a ∼ 10^{6}$ GeV, are excluded at 95% CL unless the axion-pion coupling is suppressed relative to the hadronic value.
The bound is independent of the axion-photon and axion-electron couplings, so it constrains models that stellar cooling arguments cannot reach.
The upper reach of the CAST helioscope search, roughly 1 eV, coincides with this cosmological limit, so a CAST detection in that range would be in tension with the structure-formation bound.
The same analysis pipeline reproduces $∑ m_ν < 0.65$ eV for neutrinos, giving a direct comparison of how strongly the data constrain a bosonic versus a fermionic hot relic of the same mass.
For non-hadronic models the exclusion contour shifts only through the rescaling of $C_{aπ}$, so the bound weakens in a way that can be read off directly from the two-dimensional plot.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the bound scales roughly as $C_{aπ}^2$ through the decoupling temperature, a model with $C_{aπ}$ smaller by a factor of a few would move the 1.05 eV limit up by a comparable factor, so the number is best read as a constraint on the combination $m_a$ and axion-pion coupling rather than on mass alone.
The axion density quoted here, 40 to 75 cm$^{-3}$, is below the neutrino density of about 112 cm$^{-3}$ per species, so an axion of the same mass contributes less hot dark matter than a neutrino; the tighter axion mass limit therefore reflects the bosonic distribution and the earlier decoupling as much as the abundance.
A future measurement of the axion-nucleon coupling, for instance from a next-generation supernova neutrino signal or a direct detection experiment, would fix the remaining freedom in the model and turn the contour plot into a single testable point.
If small-scale structure data improve below the $k = 0.15\ h$ Mpc$^{-1}$ cutoff used here, the Lyman-$α$ sensitivity noted for $g_* ≳ 60$ could extend the reach to lighter axions or to more weakly coupled ones.

Original abstract

Observations of the cosmological large-scale structure provide well-established neutrino mass limits. We extend this argument to thermal relic axions. We calculate the axion thermal freeze-out temperature and thus their cosmological abundance on the basis of their interaction with pions. For hadronic axions we find a new mass limit $m_a<1.05$ eV (95% CL), corresponding to a limit on the axion decay constant of $f_a>5.7\times 10^6$ GeV. For other models this constraint is significantly weakened only if the axion-pion coupling is strongly suppressed. For comparison we note that the same approach leads to $\sum m_\nu<0.65$ eV (95% CL) for neutrinos.

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.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,877 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.78 · human participants 0.01 · controlled comparison 0.13 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.91 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Observations of the cosmological large-scale structure provide well-established neutrino mass limits. We extend this argument to thermal relic axions. We calculate the axion thermal freeze-out temperature and thus their cosmological abundance on the basis of their interaction with pions. For hadronic axions we find a new mass limit $m_a<1.05$ eV (95% CL), corresponding to a limit on the axion decay constant of $f_a>5.7\times 10^6$ GeV. For other models this constraint is significantly weakened only if the axion-pion coupling is strongly suppressed. For comparison we note that the same approach leads to $\sum m_\nu<0.65$ eV (95% CL) for neutrinos.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Observations of the cosmological large-scale structure provide well-established neutrino mass limits.	background 1.00	0.05	0.02	asserted 1.00
s1	We extend this argument to thermal relic axions.	contribution 0.95	0.77	0.05	asserted 0.92
s2	We calculate the axion thermal freeze-out temperature and thus their cosmological abundance on the basis of their interaction with pions.	method 0.92	0.96	0.04	asserted 1.00
s3	For hadronic axions we find a new mass limit $m_a<1.05$ eV (95% CL), corresponding to a limit on the axion decay constant of $f_a>5.7\times 10^6$ GeV.	result 1.00	0.96	0.90	asserted 1.00
s4	For other models this constraint is significantly weakened only if the axion-pion coupling is strongly suppressed.	result 0.39	0.76	0.07	asserted 0.75
s5	For comparison we note that the same approach leads to $\sum m_\nu<0.65$ eV (95% CL) for neutrinos.	result 0.93	0.87	0.05	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.58.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** Dimensionless axion absorption rate h(µ) as defined by Eq. (9)

**Figure 2.** Effective number of thermal degrees of freedom in the early universe during the post-QCD epoch, assuming the particle content listed in

**Figure 3.** Average axion absorption rate for fa = 107 GeV and cosmic expansion rate as a function of the cosmic temperature. Rates are in units of T 2/mPl

**Figure 4.** Axion freeze-out, assuming the a-π coupling of Eq. (5). Top: Decoupling temperature. Middle: Corresponding g∗. Bottom: Present-day axion density

**Figure 5.** Likelihood contours for the allowed axion parameters. Everything to the right of the dark shaded region is excluded at the 68% CL, and everything to the right of the light shaded region is excluded at the 95% CL. Contours of equal axion mass with the indicated ma values in eV are shown as dashed lines. Upper panel: All data included. Lower panel: Lyman-α data excluded. In

**Figure 6.** Likelihood contours including all data, equivalent to the upper panel of

**Figure 7.** Likelihood contours including all data, equivalent to the upper panel of

**Figure 8.** One-dimensional likelihood analysis for the hadronic axion model obeying Eq. (1). Shown is ∆χ 2 = χ 2 − χ 2 0 as a function of ma where χ 2 0 refers to the best-fit model. In this 1D analysis the 95% excluded region is at ∆χ 2 > 4, and the 68% excluded region at ∆χ 2 > 1, as indicated by the horizontal dashed lines

Figures reproduced from arXiv:hep-ph/0504059 by the authors.

References

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Forward citations

Cited by 37 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Prominent enhancement of axion thermalization rate from axion-kaon interactions
hep-ph 2025-05 conditional novelty 7.0 of 10

Axion-kaon scattering, previously omitted from axion thermalization calculations, exceeds the axion-pion channel near T=130 MeV and tightens the Planck Delta N_eff bound on f_a by about 30%.
Dark matter from an even lighter QCD axion: trapped misalignment
hep-ph 2021-02 conditional novelty 7.0 of 10

A Z_N-symmetric QCD axion, first trapped in a false high-temperature minimum and then oscillating about the true one, can supply the observed dark matter across a wide mass range while solving the strong CP problem.
Beyond thermal approximations: Precise cosmological bounds on Axion-Like Particles
astro-ph.CO 2026-02 conditional novelty 6.0 of 10

Solving the momentum-dependent Boltzmann equation and propagating the exact non-thermal ALP spectrum into CMB analyses yields 95% limits f_a>1.63e6 GeV (e), 9.41e6 GeV (mu), 8.06e4 GeV (tau), and g_a_gamma<1.98e-8 GeV^-1.
Improved cosmological constraints on axion-lepton interactions
hep-ph 2025-11 conditional novelty 6.0 of 10

For axion masses above 0.1 eV, cosmology provides the strongest known limits on axion couplings to muons, taus, and flavor-violating tau channels, excluding decay constants up to 10^8 GeV.
The Irreducible Axion Background
hep-ph 2022-09 accept novelty 6.0 of 10

An irreducible freeze-in axion abundance, computed at the minimal BBN-consistent reheat temperature, exceeds the level allowed by dark-matter decay searches and yields bounds on axion couplings three to four orders of...

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Thermal axion production at low temperatures: a smooth treatment of the QCD phase transition
hep-ph 2021-08 conditional novelty 6.0 of 10

A spline-joined thermal axion production rate above and below the QCD confinement scale gives a continuous delta N_eff prediction that future CMB-S4 surveys could test.
Breakdown of chiral perturbation theory for the axion hot dark matter bound
hep-ph 2021-01 conditional novelty 6.0 of 10

The widely quoted hot dark matter bound on the axion mass, about 1 eV, is not trustworthy because the chiral expansion used to derive it breaks down at the temperatures that set the bound.
The Cosmic Axion Background
hep-ph 2021-01 conditional novelty 6.0 of 10

Relativistic axions from the early universe, or from decaying dark matter, could be detected by repurposing existing axion dark matter experiments, with decaying dark matter already within projected reach of ADMX data.
The DFSZ axion in the CMB
hep-ph 2020-12 conditional novelty 6.0 of 10

Planck and BAO data bound the DFSZ QCD axion mass below about 0.2 eV at 95 percent confidence for maximal axion-pion coupling, relaxing to 0.6 eV in DFSZ-II and effectively vanishing in DFSZ-I when that coupling is small.
Improved axion emissivity from a supernova via nucleon-nucleon bremsstrahlung
hep-ph 2019-06 accept novelty 6.0 of 10

Including finite pion mass, rho-meson exchange, in-medium nucleon masses, and multiple scattering reduces the supernova axion bremsstrahlung emissivity by an order of magnitude, relaxing the SN 1987A axion mass bound ...
Axion global fits with Peccei-Quinn symmetry breaking before inflation using GAMBIT
hep-ph 2018-10 conditional novelty 6.0 of 10

Global fits combining laboratory, astrophysical, and cosmological constraints on axions find a preferred QCD axion mass near 100 microelectronvolts and suggest axions are a subdominant dark matter component, with boun...
Axion cosmology with long-lived domain walls
hep-ph 2012-07 conditional novelty 6.0 of 10

Lattice simulations show long-lived axion domain walls radiate mildly relativistic axions, overproducing cold dark matter and excluding post-inflationary models with domain wall number greater than one unless the bias...
Cosmological bounds on sub-MeV mass axions
hep-ph 2010-11 conditional novelty 6.0 of 10

Cosmology excludes axions with masses between 0.7 eV and 300 keV because their decays would dilute baryons after big-bang nucleosynthesis and suppress primordial deuterium.
Getting the most on supernova axions
hep-ph 2023-06 accept novelty 5.0 of 10

Combining supernova cooling and Kamiokande-II event arguments excludes ALP-nucleon couplings above roughly 10^-9 for masses below 1 MeV, and canonical QCD axion masses above roughly 10^-2 eV.
Cosmological Bound on the QCD Axion Mass, Redux
astro-ph.CO 2022-05 accept novelty 5.0 of 10

Improved thermal axion production rates tighten the cosmological upper bound on the QCD axion mass to about 0.28 eV at 95% confidence, roughly five times stronger than prior limits.
Axion signatures from supernova explosions through the nucleon electric-dipole portal
hep-ph 2022-03 conditional novelty 5.0 of 10

Supernova axion emission through the nucleon EDM portal is bounded to gd < 6.7e-9 GeV^-2 by SN 1987A, and a supernova within about 1 kpc could yield a handful of detectable gamma-ray events in Hyper-Kamiokande.
Thermal QCD Axions across Thresholds
hep-ph 2021-08 conditional novelty 5.0 of 10

Smoothly matching thermal axion production across the heavy-fermion, heavy-Higgs, electroweak and QCD thresholds yields ΔNeff predictions that future CMB-S4 surveys can test for axion decay constants up to a few times...
Cosmic Imprints of XENON1T Axions
hep-ph 2020-07 conditional novelty 5.0 of 10

If the XENON1T electron excess comes from solar axions, those axions would contribute Delta N_eff above 0.03 to 0.04 of dark radiation, within reach of CMB-S4.
Axion hot dark matter bounds after Planck
astro-ph.CO 2013-07 accept novelty 5.0 of 10

Thermally produced axions must be lighter than 0.67 eV at 95% C.L. when Planck, WMAP, SDSS-DR7 and local H0 data are combined, and lighter than 1.01 eV from CMB data alone.
A theory of extra radiation in the Universe
hep-ph 2010-10 conditional novelty 5.0 of 10

A light chiral fermion with a TeV-suppressed coupling to standard-model particles is a viable dark-radiation candidate that satisfies astrophysical bounds and appears naturally in an E6-inspired grand unified theory.
Probing eV-scale axions with CAST
hep-ex 2008-10 accept novelty 5.0 of 10

Filling the CAST magnet bores with helium-4 gas and scanning 160 pressure settings up to 0.39 eV, the collaboration sees no solar axion signal and sets a 95% CL upper limit of about 2.2e-10 GeV^-1 on the axion-photon ...
Axion constraints in non-standard thermal histories
astro-ph 2007-11 conditional novelty 5.0 of 10

Low-temperature reheating suppresses thermal axion abundances, relaxing cosmological axion mass limits from about 1 eV up to roughly 1.4 keV for reheating temperatures near 10 MeV.
An improved cosmological bound on the thermal axion mass
astro-ph 2007-05 conditional novelty 5.0 of 10

Joint fits to WMAP, SDSS, supernova and Lyman-alpha data push the thermal hadronic axion mass below 0.42 eV at 95 percent confidence, tightening to 0.38 eV if neutrinos follow an inverted hierarchy.
A Telescope Search for Decaying Relic Axions
astro-ph 2006-11 conditional novelty 5.0 of 10

No axion decay line was found in VIMOS integral-field spectra of Abell 2667 and Abell 2390, giving upper limits of 0.003 to 0.017 on the axion two-photon coupling for masses 4.5 to 7.7 eV.
The Interplay between the Dark Matter Axion and Primordial Black Holes
astro-ph.CO 2022-09 conditional novelty 4.0 of 10

A brief era of primordial-black-hole domination dilutes the QCD axion dark matter abundance, lowering the axion mass required to match the observed dark matter density by up to three orders of magnitude.
New cosmological bounds on hot relics: Axions $\&$ Neutrinos
astro-ph.CO 2020-11 conditional novelty 4.0 of 10

Cosmological data bound the thermal axion mass below 0.91 eV and the sum of neutrino masses below 0.105 eV at 95% confidence when axions thermalize through pion scattering.
Neutrino and axion hot dark matter bounds after WMAP-7
astro-ph.CO 2010-04 accept novelty 4.0 of 10

Combining WMAP-7, the SDSS-DR7 halo power spectrum and HST, the authors set 95% upper limits of 0.41 eV on the neutrino mass sum and 0.72 eV on the hadronic axion mass when both are varied.
Isocurvature forecast in the anthropic axion window
hep-ph 2009-04 accept novelty 4.0 of 10

Existing CMB data bound axion-type isocurvature below 9 percent, and Planck or a cosmic-variance-limited probe could tighten that to 4.2 or 1.7 percent, mapping the surviving axion parameter space.
Cosmological constraints on a light non-thermal sterile neutrino
astro-ph 2008-12 conditional novelty 4.0 of 10

Cosmological data require a fourth thermalized neutrino to be lighter than about 0.4 eV at 2 sigma, and a 2 eV sterile neutrino survives at 3 sigma only if it is under-abundant or cooler than active neutrinos.
Cosmological constraints on neutrino plus axion hot dark matter
astro-ph 2007-06 accept novelty 4.0 of 10

Cosmological data excluding the Lyman-alpha forest give m_a < 1.2 eV (95% C.L.) for thermal hadronic axions and sum(m_nu) < 0.65 eV (95% C.L.) when axions are absent, with the two hot dark matter components behaving a...
An improved limit on the axion-photon coupling from the CAST experiment
hep-ex 2007-02 accept novelty 4.0 of 10

CAST's 2004 run with three improved X-ray detectors sets g_a-gamma < 8.8 x 10^-11 GeV^-1 at 95% CL for axion masses below 0.02 eV, the best laboratory limit at the time and tighter than the globular-cluster bound.
Dark Radiation candidates after Planck
astro-ph.CO 2013-04 conditional novelty 3.0 of 10

Planck's 2013 constraint on the effective number of relativistic species translates into upper bounds on sterile neutrino mixing angles, a preference against thermal axions above 0.4 eV, and limits on dark-sector degr...
The Low-Energy Frontier of Particle Physics
hep-ph 2010-02 accept novelty 3.0 of 10

Sub-eV particles with extremely weak photon couplings are motivated by both the strong CP problem and string compactifications, and a generation of laser, cavity, helioscope and fifth-force experiments can now probe w...
Dark Matter Candidates: A Ten-Point Test
astro-ph 2007-11 conditional novelty 3.0 of 10

The paper defines ten necessary tests for a dark matter candidate and grades sixteen proposed particles against them, concluding that most survive while charged CHAMPs and the first Kaluza-Klein graviton do not.
Axion Cosmology
astro-ph.CO 2015-10 accept novelty 2.0 of 10

Axions can act as dark matter, dark energy, or dark radiation depending on mass, and existing cosmological data already exclude a single ultralight axion species below about 10^-24 eV from composing all of the dark matter.
Axions : Theory and Cosmological Role
hep-ph 2013-01 accept novelty 2.0 of 10

A 2013 review concluding that if the Peccei-Quinn symmetry broke after inflation, cold axions radiated by cosmic strings and domain walls cap the axion decay constant near 2 to 4 times 10^10 GeV.
Massive neutrinos and cosmology
astro-ph 2006-03 accept novelty 1.0 of 10

A detailed review of how cosmological observations bound the sum of neutrino masses through the free-streaming suppression of small-scale structure, and of future sensitivity forecasts.

How later papers used it

60 later papers cite it

Evidence: substantial. 51 of the citing papers share no author with it, and 11 of those carry a confident label from Pith's citation classifier.

Pith read 16 of the 108 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

3 later papers by other authors are listed below: 2 used its method or tool, 1 used its data or values and 1 compared its own results with it. 1 of them appears under more than one label. 3 more papers by the same authors are listed: 1 used its method or tool and 2 compared their own results with it.

Uses its method or tool 3 papers · 1 by the same authors

The crucial quantity that is needed to extract the HDM bound is the axion decoupling temperature, $T_D$, obtained via the freeze-out condition (following the same criterium as in [ref] ) [equation] Here, $H(T) = √(4π^3 g_⋆(T) / 45) T^2 / m_pl$ is the Hubble rate (assuming a radiation dominated Universe) in terms of the Planck mass $m_pl = 1.22 ×10^19$ GeV and the effective number of relativistic degrees of freedom, $g_⋆(T)$, while $Γ_a$ is the axion thermalization rate entering the Boltzmann equation [equation] where $n_a^eq = (ζ_3 / π^2) T^3$ and $f_i = 1/(e^E_i/T - 1)$.

Breakdown of chiral perturbation theory for the axion hot dark matter bound (2021) · Introduction · 0.94
For the perturbative calculation up to NLO, we expand the squared amplitude as $∑|ℳ|^2≃∑|ℳ^(2)|^2+∑2ℳ^(2)Re(ℳ^(4))$, and then the perturbative axion rate will be casted into the following form [ref] [equation] where the dimensionless functions $h_lo$ and $h_nlo$ denote the contributions from $∑|ℳ^(2)|^2$ and $∑2Re(ℳ^(2)ℳ^(4))$, respectively.

Axion-pion scattering at finite temperature in chiral perturbation theory and its influence in axion thermalization (2023) · Brief discussions on the axion thermalization rate and its cosmology implication · 0.96

By the same authors

Limited itself to the traditional treatment of axion thermalization presented in this paper.

Thermal axions with multi-eV masses are possible in low-reheating scenarios (2021) (same authors) · 0.94 · paraphrased: the licence does not allow quoting

Uses its data or values 1 of 5 papers with this label

Used the hadronic axion upper mass bound of about 1.05 eV quoted in this paper.

An improved cosmological bound on the thermal axion mass (2007) · 0.87 · paraphrased: the licence does not allow quoting

Compares with it 3 of 5 papers with this label · 2 by the same authors

We have checked that $h_LO$ reproduces the result of Ref. [ref] within percent accuracy.

Breakdown of chiral perturbation theory for the axion hot dark matter bound (2021) · Introduction · 1.00

By the same authors

Said that its latest limit on the axion mass is almost identical to one that some of its authors derived several years ago in this paper.

Axion hot dark matter bounds (2008) (same authors) · 0.97 · paraphrased: the licence does not allow quoting
Said that its axion mass limit of 1.4 eV in the absence of neutrino masses is significantly weaker than the 1.05 eV limit found earlier in this paper.

Cosmological constraints on neutrino plus axion hot dark matter (2007) (same authors) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

55 arXiv papers cite this in 100 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 62 sentences without a confident label

Builds on it 2 papers

We return to this topic to extend previous studies by some of us [ref] in several ways.

Cosmological constraints on neutrino plus axion hot dark matter · Introduction · 0.99
This figure can also be applied to thermally produced axions, like in Refs. [ref] .

Cosmological constraints on a light non-thermal sterile neutrino · Mass/temperature bounds in the thermal case · 0.85

Uses its method or tool 3 papers

Therefore, we limit ourselves to the traditional treatment of axion thermalization presented in [ref] and comment later on this important point.

Thermal axions with multi-eV masses are possible in low-reheating scenarios · Axion decoupling in standard cosmology · 0.94
The crucial quantity that is needed to extract the HDM bound is the axion decoupling temperature, $T_D$, obtained via the freeze-out condition (following the same criterium as in [ref] ) [equation] Here, $H(T) = √(4π^3 g_⋆(T) / 45) T^2 / m_pl$ is the Hubble rate (assuming a radiation dominated Universe) in terms of the Planck mass $m_pl = 1.22 ×10^19$ GeV and the effective number of relativistic degrees of freedom, $g_⋆(T)$, while $Γ_a$ is the axion thermalization rate entering the Boltzmann equation [equation] where $n_a^eq = (ζ_3 / π^2) T^3$ and $f_i = 1/(e^E_i/T - 1)$.

Breakdown of chiral perturbation theory for the axion hot dark matter bound · Introduction · 0.94
The explicit freeze out condition advocated in Ref. [ref] to determine the axion decoupling temperature is [equation] where $H(T)=T^2√(4π^3g_*(T)/45)/m_Pl$ denotes the Hubble expansion parameter, with $g_*(T)$ the effective number of relativistic thermal degrees of freedom (d.o.f) and $m_Pl$ the Plank mass. $Γ_a(T)$ in Eq. [ref] stands for the averaged axion thermalization rate in the pion thermal bath, and it can be calculated via [equation] where the sum runs over all the possible $aπ$ reaction channels, the axion number density in equilibrium is $n_a^eq=ζ(3) T^3/π^2$ with $ζ$ the Riemann Zeta function, and the phase space integral is [equation] The recipe given in Ref [ref] will be used to calculate the above phase space integral.

Axion-pion scattering at finite temperature in chiral perturbation theory and its influence in axion thermalization · Brief discussions on the axion thermalization rate and its cosmology implication · 0.97

Uses its data or values 5 papers

The thermally averaged rates for these processes were first computed by [ref] and updated by [ref] , which found [equation] where $x_π ≡m_π/T$, $A=0.215$ and $h(x)$ is a numerical function normalized to $h(0)=1$ that decays exponentially below $T=m_π$ (see Appendix [ref]).

The DFSZ axion in the CMB · Interactions with pions · 0.83
For instance, for the hadronic axion upper mass bound quoted in Ref. [ref] , i.e. $m_a∼1.05$ eV, the axion decouples at $T_D∼64$ MeV, at which $g_⋆S(T_D)≃15.24$ and $Ω_ah^2 ≃0.0053$.

An improved cosmological bound on the thermal axion mass · Cosmological Constraints · 0.87
The processes to consider are $π^0π^±→a π^±$ and $π^+π^-→a π^0$, with an approximate total scattering rate for both given by [ref] :

New cosmological bounds on axions in the XENON1T window · Background · 0.84

Compares with it 4 papers

Numerically our latest limit on $m_a$ [ref] is almost identical to one that some of us have derived several years ago [ref] .

Axion hot dark matter bounds · Introduction · 0.97
Our neutrino mass bound $∑m_ν<0.65$ eV (95% C.L.) in the absence of axions is identical to that derived by some of us in Ref. [ref] , whereas the axion mass limit $m_a<1.4$ eV in the absence of neutrino masses found here is significantly weaker than the $1.05$ eV limit found earlier [ref] .

Cosmological constraints on neutrino plus axion hot dark matter · Results · 1.00
We have checked that $h_LO$ reproduces the result of Ref. [ref] within percent accuracy.

Breakdown of chiral perturbation theory for the axion hot dark matter bound · Introduction · 1.00

Cites it as support 1 paper

Before proceeding let us stress that we can neglect production processes like $ππ→π$ in the primordial hot hadronic gas [ref] because of the $$ limit [ref].

Axions and saxions from the primordial supersymmetric plasma and extra radiation signatures · Thermal axion production · 0.97

Cites it as background 18 papers

The LO calculation was performed in Refs. [ref] , while Ref. [ref] considered the impact of NLO corrections in order to assess the convergence of the chiral expansion.

Axion-pion thermalization rate in unitarized NLO chiral perturbation theory · Introduction · 0.89
From the standpoint of the axion solution to the strong CP problem, an unavoidable process arises from the model-independent coupling to gluons, $α_s/8π a/f_a G G̃$.[Other thermalization channels arise from model-dependent axion couplings to photons [ref] , SM quarks [ref] and leptons [ref] .] For $T_D ≳1$ GeV thermal axion production proceeds via its scatterings with gluons in the quark-gluon plasma [ref] , while for $T_D ≲1$ GeV processes involving pions and nucleons must be considered [ref] .

Breakdown of chiral perturbation theory for the axion hot dark matter bound · Introduction · 0.89
Quantifying the production rate across the QCD phase transition (QCDPT) in the strongly coupled regime is far from being straightforward, and axion production was analyzed either exclusively above the confinement scale [ref] or below [ref] .

Thermal axion production at low temperatures: a smooth treatment of the QCD phase transition · Introduction · 0.82

Discussion

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