Quantum break in models of axion dark matter

R. F. Sawyer

REVIEW 4 major objections 6 minor 50 references

Quantum break in models of axion dark matter

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper claims that a pure coherent axion dark-matter cloud, with no seed, converts to photon pairs in a quantum break, and that many photon modes prevent the cosmological red shift from stopping the conversion.

desk verdict A clever MMF treatment with a genuine zero-parameter check at small N, but the headline synchronization claim rests on an ad hoc red-shift sweep that contradicts its own definition and is likely an artifact. read the letter →

arxiv 1908.04298 v1 pith:KPFXZO2W submitted 2019-08-12 hep-ph

R. F. Sawyer This is my paper · ORCID

classification hep-ph

keywords axiondarkmatterquantumbreakaxion-photonconversionmodifiedmean-fieldapproximationparametricinstabilityred-shiftsynchronizationphotonpairproductioncompositeoperators

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that a homogeneous, coherent cloud of axions—the kind often invoked as dark matter—does not need a small pre-existing photon 'seed' to decay. Through a quantum break, the axion field converts almost completely into pairs of photons after a gestation time of order $r_g^{-1}\log(\rho m_a^{-4})$, where $r_g$ is the axion–photon growth rate and $\rho m_a^{-4}$ counts how many nearly-resonant photon pair states are available. The mechanism is carried by a modified mean-field treatment that keeps quantum correlations among axion, photon-pair, and photon-number operators that a classical treatment discards. Adding many photon modes shortens the logarithmic waiting time to $\log(N_a/N_d)$ and makes the conversion robust to the red-shifting that would otherwise detune photons from the axion mass. If right, this changes how axion dark matter searches should think about axion decay: the produced state is not a classical electromagnetic wave but a macroscopic quantum superposition.

What carries the argument

The central object is the 'modified mean-field' (MMF) closure. Instead of factorizing products of the photon operators $b,c_j,d_j$, the equations of motion are written in composite operators $Z=b$, $Y_j=c_j d_j$, $X_j=c_j^\dagger c_j+d_j^\dagger d_j$, and products such as $X_j z$ and $z y_j^\dagger$ are replaced by products of expectation values in the scaled equations (5). The one quantum term $N_a^{-1}$ in the $y_j$ equation survives the factorization and provides the seed that a classical treatment must put in by hand. The instability window $|\bar\omega|<\sqrt{2}$ follows from linearizing these equations around $z=1$. The same approximation, validated against exact few-mode solutions, is then used with $N_d$ modes and with the red shift encoded as the time-dependent detuning (7).

What would settle it

Solve the full few-mode Schrödinger system (6) for $N_a=4096$ or larger and compare the turnover time with the MMF prediction $\zeta(T)\approx \log_{10}N_a$: if the exact curve stops showing equal logarithmic spacings, or the conversion does not complete, the MMF extrapolation fails. A second, observational test: if recombination-era axions heavier than about $10^{-11}$ eV produce the predicted large-scale photon flux within tens of years, and survey data show no such burst, the scenario is dead.

Watch

Extended reading notes

Core claim

Within the modified mean-field approximation, a pure axion condensate at rest with $N_a$ axions in one mode evolves through a long near-stationary gestation phase and then quickly turns most axions into photon pairs, with turnover time scaling as $r_g^{-1}\log N_a$ in the one-mode case. The same composite-operator equations give a zero-parameter match to exact Schrödinger dynamics for $N_a$ up to 1024. For $N_d$ photon modes the logarithmic factor becomes $\log(N_a/N_d)$. When a time-dependent energy mismatch $\bar\omega_j(s)$ models the cosmological red shift, a single mode is choked off once the red-shift parameter exceeds unity, but a dense set of modes inside the instability window synchronizes through intermediate processes ($\gamma_q+\gamma_{-q}\to a\to\gamma_p+\gamma_{-p}$) and again reaches near-total conversion, with the peak appearing at nearly the unredshifted mixing time. The resulting electromagnetic state has zero expectation value for the electric field while having the correct energy density, so it is a quantum superposition of nearly classical macroscopic configurations, not a classical field.

Load-bearing premise

The load-bearing premise is that the modified mean-field factorization of $X_j,Y_j,Z$ expectations stays accurate when the axion number is far larger than the values (up to 1024) where it was checked against exact quantum dynamics.

Editorial extensions

If this is right

Pure axion dark-matter condensates can convert to photons without any seed; the conversion time has no free mixing parameter at leading logarithmic order.
The more photon channels inside the instability window, the faster and more complete the break, with the effective particle number in the logarithmic delay reduced from $N_a$ to $N_a/N_d$.
Red shift is not a barrier: a broad set of unstable modes re-synchronizes the conversion, so the naive argument that red-shifted photons lose their ability to stimulate further extraction does not apply.
The produced field is non-classical in a measurable way: the electric field expectation vanishes while the photon energy density is large, so a classical electromagnetic description of the decay product is inadequate.
In the recombination-era scenario, full-strength conversion would produce a strong photon signal within tens of years of the plasma-frequency drop; the absence of that signal would tighten bounds on the axion mass and coupling.

Reading between the lines

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

A testable extension of the synchronization mechanism: the same red-shift-detuning problem afflicts any parametric resonance in an expanding background, and the $N_d$-mode equations give a minimal model for how many channels can rescue a resonance that a single mode cannot sustain.
The cheapest check of the whole framework is numerical: continue the exact few-mode dynamics to $N_a\sim10^4$–$10^5$; if the turnover time stops following the logarithmic spacing seen below 1024, the MMF closure is an artifact of the tested range.
If the recombination-era prediction fails because some omitted process cuts conversion short, the scenario would still leave a diffuse, phase-incoherent photon background—an observational signature distinct from a coherent burst.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

You should know two things about this paper. First, there is a real idea here: the modified mean-field (MMF) closure is tested against exact Schrödinger dynamics for Na up to 1024, and the zero-parameter agreement in Fig. 1 is impressive. That part is worth taking seriously. Second, the paper's most dramatic claim—that many photon modes synchronize to nullify cosmological red-shift—is built on an equation that is physically wrong. I would not trust the synchronization peak in Fig. 5 until that is fixed.

The genuinely good part is the MMF approach itself. The comparison to exact small-N calculations is a real zero-parameter check, not a fit, and the idea that multiple modes replace log(Na) with log(Na/Nd) is plausible and cleanly illustrated. The paper is honest about its limitations, going so far as to say "everything remains a bit tentative." That honesty is welcome.

The soft spot is load-bearing. Equation (7) defines the red-shift profile as omega_j(s) = omega_j(0)(s/S - 1/2) xi. But the paper defines xi as the fraction of energy a photon loses between s=0 and S. A physical photon that loses energy has a monotonically decreasing detuning; Eq. (7) instead forces every mode to sweep through resonance at mid-course and then blue-shift to positive detuning at late times. That is not what cosmology does. It manufactures the synchronization by hand. The stress-test note is correct: a monotone red-shift would choke the conversion for all modes at once, and the clever "countless small denominators" argument in Sec. 4 never recovers from this.

The other weaknesses are more minor in comparison. The extrapolation from Na ≤ 1024 to astrophysical Na is a leap even if the MMF closure is accepted; no argument is given for why the closure holds at 10^9 or beyond. The estimate of Nd is also order-of-magnitude at best. But these are secondary. If Eq. (7) were replaced with a real cosmological red-shift, the synchronization claim would likely disappear, and the paper would fall back to the more modest but still interesting result about quantum break and mode-number reduction.

Who is this for? Someone working on axion dark matter or quantum break phenomena might want to read the MMF development, but they should skip Sec. 4 unless it is revised. The paper deserves a serious referee because the small-N check and the MMF idea are worth engaging with, and a good referee can pinpoint exactly why the red-shift model fails. I would not cite it in its current form. Bring it to reading group only if you want a case study in how an appealing synchronization narrative can be an artifact of a bad modeling choice.

Referee Report

4 major / 6 minor

Summary. The paper develops a modified mean-field (MMF) treatment of axion-photon conversion starting from a pure axion condensate at rest, using composite operators (Z, Y_j, X_j) to avoid postulating a classical seed. It claims that a 'quantum break' occurs on a time scale of order r_g^{-1} log(ρ m_a^{-4}), that the logarithm is reduced when many photon modes are included, and that including a multiplicity of modes within the instability window produces a 'synchronization' effect that appears to nullify the conventional cosmological red-shift limitation on the conversion. The MMF closure is tested against exact few-mode Schrödinger dynamics for N_a ≤ 1024 (Fig. 1), and then applied to much larger N_a, including N_a = 5×10^5 with up to N_d = 5000 modes in the red-shift calculation (Figs. 5 and 6). The paper ends with a speculative application to axion dark matter at recombination.

Significance. If the synchronization claim were established, the paper would be significant: it would imply that axion-photon conversion can proceed efficiently without seeds on cosmologically relevant time scales, potentially producing observable photon signals or new exclusion bounds on axion couplings. The zero-parameter small-N comparison in Fig. 1 is a genuine strength, and the paper is candid about the tentative status of its large-N extrapolations. However, the central astrophysical claim rests on an ad hoc red-shift profile and on an unvalidated mean-field closure at astrophysical particle numbers; the significance is therefore conditional on substantial further work.

major comments (4)

[Sec. 4, Eq. (7)] The red-shift profile (7) is inconsistent with its own definition of ξ and with physical cosmology. The text defines ξ as the fraction of energy a photon loses between s=0 and s=S, so a photon initially at energy m_a/2 should have negative detuning at late times and its detuning should decrease monotonically. Equation (7) instead gives ωbar_j(s) = ωbar_j(0)(s/S − 1/2)ξ, which vanishes at s=S/2 and becomes positive (blue-shifted) for s>S/2; for ωbar_j(0)>0 the detuning starts negative and increases through zero, the opposite of a physical red shift. Moreover, ξ=5 is used in Fig. 5, which as a fractional energy loss is unphysical (a photon cannot lose 500% of its initial energy). Since the synchronization peak in Fig. 5 is driven entirely by this artificial simultaneous resonance crossing, the claim that multiple modes 'nullify' red-shift limitations is unsupported. The calculation should be redone with a physically motivated profile, e.g., ωbar_j(s) = (m_a/2)(a(0)/a(s) − 1) + ωbar_j(0)a(0)/a(s), with a monotone scale factor.
[Sec. 2, after Eq. (5); Figs. 1 and 2] The MMF closure — replacing expectation values of products of X_j, Y_j, Z by products of expectation values — is validated only against exact solutions for N_a ≤ 1024. The paper then applies the same closure at N_a = 10^9 (Fig. 2) and N_a = 5×10^5 (Figs. 5–6) without an independent check. The logarithmic growth law and, more importantly, the synchronization effect at large N_a,N_d are therefore not established. The authors themselves note that 'everything remains a bit tentative' and call for better computing power. To support the astrophysical extrapolation, a test at an intermediate N_a beyond the current exact range, or a comparison with an alternative approximation (e.g., truncated Wigner or a controlled large-N expansion), is needed.
[Sec. 3, mode-number estimate] The replacement of the logarithm log N_a by log(ρ m_a^{-4}) is asserted without a derivation. The counting of modes N_d that satisfy both the periodic-box boundary conditions and energy conservation to within ΔE T << 1 is only sketched, yet this counting determines the claimed order-of-magnitude shortening of the mixing time. The paper should provide the explicit scaling of N_d with box volume, momentum resolution, and axion parameters, and justify why N_d is effectively independent of N_a in the relevant regime.
[Sec. 4, Figs. 5–6] Even if Eq. (7) were replaced by a physical red-shift model, the extrapolation from N_d = 5000 to the actual mode count in an astrophysical volume is not quantified. The model assumes a single coherent axion mode in a periodic box; for a realistic dark matter halo, the number of modes within the instability window and the coherence volume of the axion field need to be specified. Without this, the claim that 'there will be an ample supply' of modes is qualitative and cannot support a quantitative prediction such as the 'few tens of years' conversion time in Sec. 6.

minor comments (6)

[Abstract and Sec. 6] The abstract describes the produced field as 'coherent,' but Sec. 6 explains that ⟨c(t)⟩=⟨d(t)⟩=0 while the energy density is nonzero, meaning the states are number-squeezed rather than classical coherent states. Consider rewording to avoid confusion.
[Sec. 2, Eq. (6)] The matrix element ⟨α+1|H|α⟩ = λ V^{-1/2} α(N_a − α + 1)^{1/2} appears to have an index mismatch: the factor α should probably be N_a − α (or an equivalent) if α labels the number of axions remaining. Please verify the formula and the convention.
[Sec. 4, figure numbering] The text refers to 'fig. 4' for the N_d-dependence plot, but the corresponding caption is labeled 'FIG. 5'. The zoom is called 'FIG. 6' but is described as Fig. 6 in the text; please reconcile the numbering and the references.
[Sec. 5] The '20% random variations' in the axion substrate coupling are described verbally with no figure or quantitative summary. Please provide the distribution of outcomes or specify the number of realizations used.
[Sec. 3, Fig. 4] The caption for Fig. 4 says 'The same as fig. 3, but for the ordinary mean-field, or classical, model,' but the text says the conventional mean-field calculation used an initial mixing fitted to the short-time MMF result. Please state that choice explicitly in the caption.
[Sec. 1 and references] Reference [2] (Hu, Barkana, Gruzinov) is cited as Phys.Rev.Lett. 85, 1158 (2000), arXiv:astro-ph/0003365; the arXiv identifier in the reference list omits the page number but that is fine. The list contains an entry with a typo 'arXiv:1807.033222' (reference [25]) — the arXiv number has too many digits.

Circularity Check

1 steps flagged · score 6.0 of 10

The Sec. 4 red-shift 'synchronization' is imposed by Eq. (7), which forces every photon mode through exact resonance at the same time; the claimed emergent effect reduces to this choice by construction.

self definitional [Sec. 4, Eq. (7) and the discussion after Fig. 5]
"We then define ̄ωj(s) = ̄ωj(0)(s/S − 1/2)ξ (7) which encodes the mismatch between the axion environment and the red-shifted photons in a way that it vanishes midcourse. ... It is the explicit time dependence of the red-shifting term in (8) that causes cloud photons to continuously be promoted into the regions most closely tuned to the axion substrate."

The advertised multi-mode synchronization is not derived from a physical mechanism; it is written into the ansatz. Eq. (7) makes every mode's detuning vanish at the same instant, s = S/2, regardless of cosmology. The later statement that the red-shift term 'causes cloud photons to continuously be promoted into the regions most closely tuned' is therefore a restatement of the definition, not a prediction. In addition, a physical cosmological red shift is monotone in s, so the symmetric sweep through resonance, including a late-time blue-shifted branch, is an ad hoc construction. The central claim that many photon states 'nullify conventional red-shift limitations' is thus equivalent to the assumed detuning function, making that part of the paper circular.

full rationale

The modified mean-field closure is tested against exact small-N Schrodinger solutions with no fitted constants, so the quantum-break mechanism and the logarithmic time scaling in Secs. 2-3 are self-contained and non-circular. The paper's own citations to the author's prior work are background examples of quantum-break phenomena, not load-bearing derivations. However, the headline red-shift result of Sec. 4 is different: Eq. (7) defines every mode's detuning to pass linearly through zero at the same scaled time, which directly produces the synchronized conversion peak in Fig. 5. The paper even states that the effect is 'entirely a result of the red-shift induced time dependence of (7)' and concedes that 'everything remains a bit tentative.' Thus the synchronization claim is partially circular: the output (simultaneous resonance and conversion) is placed into the input detuning function by construction, rather than emerging from an independent cosmological or dynamical argument. This warrants a score of 6 rather than higher because the no-seed quantum break and the small-N validation remain independent content, and the red-shift section is explicitly exploratory.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The central claim rests on the standard axion-photon coupling, the modified mean-field factorization, and the ad hoc red-shift detuning model. No new particles or forces are introduced; the 'quantum break' is a dynamical phenomenon, not an entity.

free parameters (1)

Red-shift parameter ξ = 5 (example)
Chosen to demonstrate the synchronization effect in Sec. 4; the paper does not derive ξ from cosmology, and it is an adjustable input to the model.

assumptions (3)

domain assumption Standard axion-photon interaction L_I = gγ a E·B
This is the standard coupling from the axion literature; the paper cites refs [6]-[8] and uses it throughout.
ad hoc to paper Modified mean-field factorization: expectation values of products of X_j, Y_j, Z factorize
The central approximation is justified only by comparison to exact solutions for N_a ≤ 1024; its validity at astrophysical N_a is assumed, not proven. Introduced in Sec. 2 after Eq (5).
ad hoc to paper Red-shift detuning profile ωbar_j(s) = ωbar_j(0)(s/S - 1/2)ξ
Eq (7) encodes cosmological red-shift as a linear detuning sweep; this form is chosen by hand and is not derived from the physics of an expanding universe.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Quantum break in models of axion dark matter." pith.science (2026). https://pith.science/paper/KPFXZO2W

@misc{pith2026190804298,
  author       = {Pith},
  title        = {Pith review of: Quantum break in models of axion dark matter},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KPFXZO2W}},
  note         = {Machine review of arXiv:1908.04298}
}

read the original abstract

A system of light axions comprising a classical axion field, one candidate for dark matter, has an instability that can rapidly mix in photon pairs in a coherent fashion if initiated by a quantum break (which eliminates the need for seeds.) Adding more photon states, such as a multiplicity of angles for the case of the axion field at rest, reduces the argument of a logarithmic factor in the mixing time by orders of magnitude. Admitting multiple photon states, all within a window of instability, leads to a synchronization effect that appears to nullify conventional red-shift limitations. Even the fully developed states of the electromagnetic field produced are highly non-classical; they can be looked on as quantum superpositions of different nearly-classical macroscopic systems.

Figures

Figures reproduced from arXiv: 1908.04298 by the authors.

**Figure 2.** FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 5.** Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

**Figure 6.** Figure 6: shows a magnified view of these curves in the region of most interest. At maximum, the case with Nd = 5000 has transformed more than 1/2 of the axions to photon pairs while for Nd = 5 it is about 1/100 at maximum.This is entirely a result of the red-shift induced time …

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

50 extracted references · 23 canonical work pages

[1]

vacuum ﬂuctuation

Introduction Cosmological models in which the dark matter is composed of light axion s, in an essentially classical condensed state, have attracted attention recently [1] - [9]. Here we shall lo ok again at the time evolution due to electromagnetic interactions of a piece of this matter, consisting of Na axions contained within a periodic box of volume, V...

work page
[2]

modiﬁed mean-ﬁeld approach

The model. We deﬁne c† j, d† j to create photons with respective momenta ⃗ qj and −⃗ qj of the same helicity, and b to annihilate an axion in the original condensed mode, where we take the initial occ upation number of the mode to be Na and the axion cloud at rest. The i will be used to index a set of Nd ﬁnal states with photons that have various magnitud...

work page
[3]

resonant

Multiple mode solutions First we use the multiple beams ( j = 1 ...Nd) model solutions of (5) and conserve energy exactly, ¯ ωi = 0, as would be the case if the modes were to be a spherically symmetrical distribu tion of Nd rays. This leads to a replacement of the log Na factor in the turnover time by log[ Na/Nd], with the other factors essentially unchan...

work page
[4]

We begin by turning on t he coupling, taking local t=0, everywhere, at a particular value of the local red-shift

Red shift eﬀects In a cosmological application we envision ourselves awaiting a pulse of p hotons that was initiated at a time T in the past, where T is the axion-photon mixing time. We begin by turning on t he coupling, taking local t=0, everywhere, at a particular value of the local red-shift. Now the problem is that t he initial mixings, being partly a...

work page
[5]

Save the tr ouble and take the continuum limit to get back essentially to (5)

Time boxes and inhomogeneities. Next we do a calculation in time boxes, dividing the total time interval T into 20 equal segments, taking T to be of the order of the expected mixing time in the monolithic calculation. We t hen solve for the complete time region by computing values on each segment boundary to use as an initial value on the following bounda...

work page
[6]

L. Hui, J. P. Ostriker, S. Tremaine, E. Witten, Phys. Rev. D95 , 043541 (2017); arXiv:1610.08297

arXiv 2017
[7]

W. Hu, R. Barkana, A. Gruzinov, Phys.Rev.Lett. 85, 1158 (2000), arXiv:astro-ph/0003365

arXiv 2000
[8]

Amendola, R

L. Amendola, R. Barbieri, Phys.Lett. B642 (2016), 192 (2006), arXiv:hep-ph/0509257

arXiv 2016

Show all 50 references

[9]

Berlin, Phys

A. Berlin, Phys. Rev. Lett. 117, 231801 , arXiv:1608.01307

arXiv
[10]

D. J. E. Marsh, Phys. Rept. 643, 1 (2016), arXiv:1510.07633

2016 arXiv
[11]

Preskill, M

J. Preskill, M. B. Wise, F. Wilczek ,Phys.Lett. B120 , 127 (1983)

1983
[12]

Abbott and P

L. Abbott and P. Sikivie, Phys. Lett. B120, 133 (1983)

1983
[13]

M. Dine, W. Fischler, Phys.Lett. B120, 137 (1983)

1983
[14]

I. I. Tkachev, Sov. Astron. Lett. 12, 305 (1986); Phys. Lett. B191, 41 (1987)

1986
[15]

M. P. Hertzberg, JCAP 11, 037 (2016) , arXiv:1609.01342

2016 arXiv
[16]

M. P. Hertzberg, E. D. Schiappacassey, JCAP 11 , 004 (2018) , arXiv:1805.00430

2018 arXiv
[17]

Arza, arXiv:1810.03722

A. Arza, arXiv:1810.03722

arXiv
[18]

Vardi , J

A. Vardi , J. R. Anglin, Phys. Rev. Lett. 86, 568 (2001), arXiv: physics/0007054

2001 arXiv
[19]

Cametti, C

F. Cametti, C. Presilla., Phys. Rev. Lett. 89, 040403 (2002), arXiv: quant-ph/0201147

2002 arXiv
[20]

Jonathan Keeling, Phys. Rev. A 79 , 053825 (2009), cond-mat/0901.4245

2009 arXiv
[21]

R. F. Sawyer, Phys. Rev. Letters 93, 133601 ( 2004), arXiv:hep-ph/0404247

2004 arXiv
[22]

G. L. Kotkin and V. G. Serbo, Phys. Lett. B413, 122 (1997)

1997
[23]

R. F. Sawyer, Phys. Rev A89, 052321 (2014), arXiv: 1402.5170

2014 arXiv
[24]

S. S. Chakrabarty, S. Enomoto, Y. Han, P. Sikivie, E. M. T odarello, Phys. Rev. D 97 , 043531 (2018); arXiv:1710.02195

2018 arXiv
[25]

Dvali, S

G. Dvali, S. Zell, JCAP07 064 (2018); arXiv:1710.00835 [hep-ph]

2018 arXiv
[26]

Dvali, C

G. Dvali, C. Gomez, S. Zell, J. Cosmol. Astropart. Phys. 2017 no. 06, 028 ; arXiv: 1701.08776

2017 arXiv
[27]

R. F. Sawyer, Phys. Rev. Lett. 116, 081101 (2016) , arXiv:1509.03323

2016 arXiv
[28]

R. F. Sawyer, Phys. Rev. D79, 105003 (2005), arXiv: hep-ph/0503013

2005 arXiv
[29]

Izaguirre, G

I. Izaguirre, G. Raﬀelt, I. Tamborra, Phys. Rev. Lett. 118, 021101 (2017), arXiv:1610.01612

2017 arXiv
[30]

Mirizzi , M

Dasgupta , A. Mirizzi , M. Sen, arXiv:1807.033222. 8

arXiv
[31]

Capozzi , B

F. Capozzi , B. Dasgupta , A. Mirizzi, arXiv:1807.00840

arXiv
[32]

R. S. L. Hansen, A.Y. Smirnov, arXiv:1801.09751

arXiv
[33]

Vlasenko, G

A. Vlasenko, G. C. McLaughlin, Phys. Rev. D 97 , 083011 (2018), arXiv:1801.07813

2018 arXiv
[34]

Abbar, H

S. Abbar, H. Duan, arXiv:1712.07013

arXiv
[35]

Tamborra, O

M-R Wu, I. Tamborra, O. Just, H-T Janka, Phys. Rev. D 96 , 123015 (2017), arXiv:1711.00477

2017 arXiv
[36]

Dasgupta , M

B. Dasgupta , M. Sen, Phys. Rev. D 97, 023017 (2018), arXi v:1709.08671

2018 arXiv
[37]

Dighe, M

A. Dighe, M. Sen, Phys. Rev. D 97 , 043011 (2018), 1709.06858

2018 arXiv
[38]

Capozzi , B

F. Capozzi , B. Dasgupta , E. Lisi, A. Marrone, A. Mirizzi , Phys. Rev. D 96 , 043016 (2017), arXiv:1706.03360

2017 arXiv
[39]

A. Das, A. Dighe, M. Sen, JCAP 05 , 051,(2017) ; arXiv:1705.00468

2017 arXiv
[40]

Tamborra, Phys

M-R Wu, I. Tamborra, Phys. Rev. D 95 , 103007 (2017), arXiv:1701.06580

2017 arXiv
[41]

P. J. E. Peebles, Astrophys. J. 534, L127 (2009), arXiv:astro-ph/0002495

2009 arXiv
[42]

Kofman, A

L. Kofman, A. Linde, A. Starobinsky, Phys.Rev. D56, 3258 (1997)

1997
[43]

Visinelli, S

L. Visinelli, S. Baum, J. Redondo, K. Freese, F. Wilczek , Phys. Lett. 777, 64 (2017)

2017
[44]

Widdicombe,T

J.Y. Widdicombe,T. Helfer, D.J.E. Marsh, and E. A. Lim, arXiv:1806-09367
[45]

X. Du, B. Schwabe, J. C. Niemeyer, and D. Brger, Phys. Rev . D97, 063507 (2018), 1801.04864

2018 arXiv
[46]

E. W. Kolb and I. I. Tkachev , Phys.Rev. D49, 5040 (1994)

1994
[47]

D. G. Levkov, A. G. Panin, and I. I. Tkachev, (2018), 1804 .05857

2018
[48]

Luca Visinelli, arXiv: 1808.01879

arXiv
[49]

Veltmaat, J

J. Veltmaat, J. C. Niemeyer, and B. Schwabe, Phys. Rev. D98, 043509 (2018), 1804.09647

2018 arXiv
[50]

Schive, T

H.-Y. Schive, T. Chiueh, and T. Broadhurst, Nature Phys . 10, 496 (2014), 1406.6586

2014 arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

vacuum ﬂuctuation

Introduction Cosmological models in which the dark matter is composed of light axion s, in an essentially classical condensed state, have attracted attention recently [1] - [9]. Here we shall lo ok again at the time evolution due to electromagnetic interactions of a piece of this matter, consisting of Na axions contained within a periodic box of volume, V...

work page

[2] [2]

modiﬁed mean-ﬁeld approach

The model. We deﬁne c† j, d† j to create photons with respective momenta ⃗ qj and −⃗ qj of the same helicity, and b to annihilate an axion in the original condensed mode, where we take the initial occ upation number of the mode to be Na and the axion cloud at rest. The i will be used to index a set of Nd ﬁnal states with photons that have various magnitud...

work page

[3] [3]

resonant

Multiple mode solutions First we use the multiple beams ( j = 1 ...Nd) model solutions of (5) and conserve energy exactly, ¯ ωi = 0, as would be the case if the modes were to be a spherically symmetrical distribu tion of Nd rays. This leads to a replacement of the log Na factor in the turnover time by log[ Na/Nd], with the other factors essentially unchan...

work page

[4] [4]

We begin by turning on t he coupling, taking local t=0, everywhere, at a particular value of the local red-shift

Red shift eﬀects In a cosmological application we envision ourselves awaiting a pulse of p hotons that was initiated at a time T in the past, where T is the axion-photon mixing time. We begin by turning on t he coupling, taking local t=0, everywhere, at a particular value of the local red-shift. Now the problem is that t he initial mixings, being partly a...

work page

[5] [5]

Save the tr ouble and take the continuum limit to get back essentially to (5)

Time boxes and inhomogeneities. Next we do a calculation in time boxes, dividing the total time interval T into 20 equal segments, taking T to be of the order of the expected mixing time in the monolithic calculation. We t hen solve for the complete time region by computing values on each segment boundary to use as an initial value on the following bounda...

work page

[6] [6]

L. Hui, J. P. Ostriker, S. Tremaine, E. Witten, Phys. Rev. D95 , 043541 (2017); arXiv:1610.08297

arXiv 2017

[7] [7]

W. Hu, R. Barkana, A. Gruzinov, Phys.Rev.Lett. 85, 1158 (2000), arXiv:astro-ph/0003365

arXiv 2000

[8] [8]

Amendola, R

L. Amendola, R. Barbieri, Phys.Lett. B642 (2016), 192 (2006), arXiv:hep-ph/0509257

arXiv 2016