Pith. sign in

REVIEW 2 major objections 5 minor 74 references

Early matter domination dilutes multipole dark matter, reopening parameter space that standard cosmology excludes.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · grok-4.5

2026-07-10 14:45 UTC pith:CKBSRRTX

load-bearing objection Solid incremental paper: entropy dilution reopens windows for three of four multipole operators under early matter domination, with clean analytics and honest flags on the approximations. the 2 major comments →

arxiv 2607.07956 v1 pith:CKBSRRTX submitted 2026-07-08 hep-ph astro-ph.CO

Multipolar Dark Matter Freeze-out in an Early Matter-Dominated Universe

Debajit Bose , Prolay Chanda , Suvam Maharana , Poulami Mondal This is my paper
classification hep-ph astro-ph.CO
keywords multipole dark matterearly matter dominationentropy dilutionfreeze-outanapolemagnetic dipoleelectric dipolecharge radius
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Thermal dark matter's relic abundance depends on both its interactions and the early Universe's expansion history. This paper studies fermionic dark matter that couples to the Standard Model only through higher-dimensional electromagnetic operators—magnetic dipole, electric dipole, anapole, and charge-radius moments—and freezes out during an early matter-dominated epoch driven by a long-lived heavy field. Entropy injection from that field's later decay dilutes the dark-matter density, so a weaker coupling still yields the observed abundance. The resulting mass–coupling contours are compared with those of ordinary radiation-dominated freeze-out and with present direct-detection and solar-neutrino limits. The dilution reopens sizable regions, especially for the anapole interaction, that are ruled out under standard cosmology, showing that the pre-BBN thermal history can qualitatively change the experimental viability of multipole dark matter.

Core claim

Entropy dilution from an early matter-dominated era substantially lowers the multipole couplings needed to match the observed dark-matter relic density, thereby restoring viability to regions of magnetic-dipole, anapole and charge-radius parameter space that are excluded by direct detection and IceCube solar-neutrino bounds when freeze-out is assumed to occur in a radiation-dominated Universe.

What carries the argument

Analytic matter-dominated freeze-out formulae (relic density and freeze-out temperature) that incorporate the entropy-dilution factor ζ arising from the sudden decay of a heavy field ϕ; these replace the standard radiation-dominated expressions and map each multipole operator onto a lower required coupling.

Load-bearing premise

The calculation assumes freeze-out finishes while the Universe is still purely matter-dominated and entropy is conserved, before the heavy field begins to decay; if that hierarchy fails, the analytic formulae no longer apply.

What would settle it

A complete numerical solution of the coupled Boltzmann equations that includes continuous ϕ decay during freeze-out, for the same multipole operators and the same reheating temperatures, would show whether the lower-coupling contours remain viable once entropy injection is treated continuously.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper studies thermal freeze-out of fermionic dark matter that couples to the photon through dimension-5 and dimension-6 electromagnetic multipole operators (magnetic dipole, electric dipole, anapole, charge radius) in an early matter-dominated cosmology driven by a long-lived heavy field φ. Analytic solutions of the Boltzmann equation (App. A) yield the freeze-out abundance and the subsequent entropy-dilution factor ζ that relates it to the observed relic density (Eqs. 17–19). The required couplings are mapped in the (m_χ, g/Λ) or (m_χ, g/Λ^{2}) planes for several reheating temperatures and compared with radiation-dominated freeze-out and with current direct-detection and IceCube solar-neutrino limits. The central claim is that entropy dilution substantially lowers the interaction strength needed for Ωh^{2} = 0.12, reopening regions that are excluded under standard radiation domination, most notably for the anapole operator at low T_RH.

Significance. If the result holds, it shows that the pre-BBN expansion history is an essential ingredient in the phenomenology of electromagnetic multipole dark matter: regions that appear ruled out by direct detection and solar neutrinos under radiation domination become viable once entropy injection is taken into account. The work supplies explicit analytic formulae for the matter-dominated yield, carefully derived non-relativistic annihilation cross sections (App. B), and a transparent set of consistency conditions (Sec. II D) that mark where the pure-MD treatment is self-consistent. These ingredients make the qualitative conclusion falsifiable and useful for future model-building and experimental reinterpretation.

major comments (2)
  1. The analytic relic-density formulae (Eqs. 17–19) and the solid-black segments of the contours rest on the pure-MD, entropy-conserving, sudden-decay hierarchy T_f ≫ T_Γ, T_RH (Sec. II C, App. C). While the paper correctly greys out the T_f < T_Γ segments and states that a coupled evolution is then required, the quantitative size of the reopened windows for T_RH = 0.1 GeV and 10 GeV is still quoted from those formulae. A short numerical check (or an explicit statement of the residual uncertainty) for at least one benchmark point near the edge of the solid-black region would strengthen that the dilution factor remains accurate enough to support the claim that previously excluded parameter space is reopened.
  2. The analysis is restricted to m_χ < m_W to avoid the spurious high-energy growth of the W^{+}W^{-} channels (Sec. III B). This is a legitimate EFT cut, but it leaves the phenomenologically interesting multi-hundred-GeV to TeV window unexplored. Because the paper already flags the need for a full gauge-invariant basis including Z and Higgs operators, a brief estimate of how the relic contours would shift once those channels are restored (or an explicit deferral with a quantitative caveat) would clarify the scope of the “reopened” regions advertised in the abstract and Sec. IV.
minor comments (5)
  1. Abstract and Sec. IV: the phrase “confront it with current constraints” should be “confront them” (subject–verb agreement).
  2. Figs. 1 and 2: the solid-black versus grey distinction for T_f ≳ T_Γ is explained only in the caption; a short sentence in the main text of Sec. IV would help readers who look first at the figures.
  3. Table I (NR structures): the charge-radius entry lists the operator as χ̄ γ^μ γ^{5} χ J_μ, which appears to be a typographical mix-up with the anapole; the correct CR structure is the vector current without γ^{5}.
  4. Eq. (16) for g_eff^{1/2}: the approximation used later in App. A (g_eff^{1/2} ≃ (3/4) g_igstar^{1/2} (1−r)^{-½} x^{-½} x_igstar^{1/2}) is stated only after the fact; a forward reference would improve readability.
  5. Note Added: the arXiv number of the concurrent work is given as 2607.01390; a quick consistency check of the citation would avoid a possible typographical error.

Circularity Check

0 steps flagged

No significant circularity: relic contours are computed from free cosmological parameters and external Ωh², then compared to independent experimental bounds.

full rationale

The paper's central claim is that entropy dilution from early matter domination lowers the multipole couplings needed for Ωχh² = 0.12, reopening regions excluded under radiation-dominated freeze-out. The derivation chain is: (i) free parameters T⋆, r, TRH define the modified Hubble and dilution factor ζ (Eqs. 1–9, 7); (ii) multipole operators yield ⟨σv⟩ expansions (Sec. III A, App. B) that are standard EFT results; (iii) the Boltzmann equation is solved analytically under the pure-MD, sudden-decay assumptions (App. A, Eqs. 17–19) to obtain the coupling that matches the external Planck benchmark Ωh² = 0.12; (iv) the resulting contours are overlaid on external direct-detection and IceCube limits. None of these steps is self-definitional, a fitted input re-used as a prediction, or a uniqueness claim imported from the authors' prior work. Self-citations supply cross-sections or earlier multipole phenomenology but are not load-bearing for the dilution effect itself. The sudden-decay hierarchy is an explicit assumption whose breakdown is marked (gray contour segments) rather than hidden. The result is therefore a genuine parameter-space comparison, not a circular construction.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 1 invented entities

The central claim rests on standard Boltzmann cosmology plus four free cosmological parameters that control the amount of entropy dilution, together with the assumption that a single multipole operator dominates and that freeze-out occurs before significant ϕ decay. No new particles beyond the conventional long-lived heavy field ϕ are invented; the multipole operators themselves are taken from the existing EFT literature.

free parameters (4)
  • T_⋆ = 10^5 GeV
    Temperature at which the heavy field ϕ becomes matter-like; fixed by hand to 10^5 GeV for all numerical contours.
  • r = 0.99
    Radiation energy-density fraction at T_⋆; fixed to 0.99.
  • T_RH = 0.1, 10, 10^3 GeV
    Reheating temperature after ϕ decay; scanned over three discrete values (0.1, 10, 10^3 GeV) that set the entropy-dilution factor ζ.
  • g/Λ or g/Λ²
    Effective multipole coupling strength solved for so that Ωh² = 0.12; the free parameter that is mapped against experimental bounds.
axioms (5)
  • domain assumption Universe undergoes an early matter-dominated era driven by a long-lived heavy field ϕ that later decays and injects entropy before BBN.
    Sec. II; standard non-standard-cosmology premise taken from Hamdan–Unwin and related works.
  • domain assumption Sudden-decay approximation: entropy is conserved until ϕ decays instantaneously at T_Γ ≈ T_RH.
    Sec. II C and App. C; used to obtain the closed-form dilution factor ζ and the analytic yield formulae.
  • ad hoc to paper Only one multipole operator is present at a time; all other coefficients are set to zero.
    Sec. III A and IV; simplifies the scan but is not required by any UV completion.
  • domain assumption EFT description restricted to m_χ < m_W so that photon-only operators remain gauge-invariant and free of spurious energy growth.
    Sec. III B; authors explicitly acknowledge that a full SU(2)×U(1) operator basis is needed above the electroweak scale.
  • standard math Standard thermal freeze-out Boltzmann equation with NR velocity expansion of ⟨σv⟩.
    Eqs. 11–19 and App. A; textbook treatment adapted to matter-dominated Hubble expansion.
invented entities (1)
  • long-lived heavy field ϕ no independent evidence
    purpose: Drives the early matter-dominated era and supplies the entropy injection that dilutes the DM abundance.
    Standard ingredient of non-standard cosmologies; no new quantum numbers or interactions beyond those already assumed in the literature are introduced.

pith-pipeline@v1.1.0-grok45 · 28434 in / 3231 out tokens · 26497 ms · 2026-07-10T14:45:35.267535+00:00 · methodology

0 comments
read the original abstract

The relic abundance of thermal dark matter depends not only on its particle interactions but also on the expansion history of the early Universe. We study the freeze-out of fermionic dark matter interacting with the Standard Model through higher-dimensional electromagnetic operators in an early matter-dominated cosmology. In particular, we consider magnetic dipole, electric dipole, anapole, and charge-radius interactions, and compute the couplings required to reproduce the observed dark matter relic abundance in the presence of entropy injection from the decay of a long-lived heavy field. The resulting parameter space is compared with that obtained in the standard radiation-dominated freeze-out scenario and confront it with current constraints from direct-detection experiments and solar neutrino observations. We find that the entropy dilution associated with an early matter-dominated epoch significantly reduces the interaction strength required to obtain the observed relic abundance, thereby rendering viable regions of parameter space that are excluded in the conventional cosmological history. Our results demonstrate that the cosmological history prior to Big Bang nucleosynthesis can have an important impact on the phenomenology and experimental viability of electromagnetic multipole dark matter.

Figures

Figures reproduced from arXiv: 2607.07956 by Debajit Bose, Poulami Mondal, Prolay Chanda, Suvam Maharana.

Figure 1
Figure 1. Figure 1: FIG. 1. Dimension-six operators: relic density contours in [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

74 extracted references · 74 canonical work pages · 56 internal anchors

  1. [1]

    X n δχ(δχ + 2)λnx−n−2 f g1/2 eff # Yχ,eq(xf). (A12) Substituting for the equilibrium abundanceY χ,eq from Eq. (12) and using 1− 3 2xf ≈1, we obtain xf = ln b

    Calculation for the freeze-out temperature At freeze-out the DM relic abundance stop tracking the equilibrium abundance, hence, ∆χ(xf)≃Y χ,eq(xf) =δ χYχ,eq(xf), (A9) whereδ χ is a order of unity factor. Neglectingd∆ χ/dxnear freeze-out, from Eq. (A2) we may write dYχ dx f ≈ − X n λn δχ(δχ + 2)x −n−2 f g1/2 eff (xf)Y 2 χ,eq(xf). (A10) Also, dYχ,eq dx =Y χ,...

    work page

  2. [2]

    The First Three Seconds: a Review of Possible Expansion Histories of the Early Universe

    R. Allahverdiet al., The First Three Seconds: a Re- view of Possible Expansion Histories of the Early Uni- verse, Open J. Astrophys.4, astro.2006.16182 (2021), arXiv:2006.16182 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  3. [3]

    Kamionkowski and M

    M. Kamionkowski and M. S. Turner, Thermal Relics: Do We Know Their Abundances?, Phys. Rev. D42, 3310 (1990)

    work page 1990

  4. [4]

    G. F. Giudice, E. W. Kolb, and A. Riotto, Largest tem- perature of the radiation era and its cosmological im- plications, Phys. Rev. D64, 023508 (2001), arXiv:hep- ph/0005123

    work page arXiv 2001

  5. [5]

    Wino Cold Dark Matter from Anomaly-Mediated SUSY Breaking

    T. Moroi and L. Randall, Wino cold dark matter from anomaly mediated SUSY breaking, Nucl. Phys. B570, 455 (2000), arXiv:hep-ph/9906527

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  6. [6]

    D. H. Lyth, Dilution of cosmological densities by sax- ino decay, Phys. Rev. D48, 4523 (1993), arXiv:hep- ph/9306293

    work page arXiv 1993

  7. [7]

    The effect of a late decaying scalar on the neutralino relic density

    G. Gelmini, P. Gondolo, A. Soldatenko, and C. E. Ya- guna, The Effect of a late decaying scalar on the neu- tralino relic density, Phys. Rev. D74, 083514 (2006), arXiv:hep-ph/0605016

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  8. [8]

    G. B. Gelmini and P. Gondolo, Neutralino with the right cold dark matter abundance in (almost) any su- persymmetric model, Phys. Rev. D74, 023510 (2006), arXiv:hep-ph/0602230

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  9. [9]

    B. S. Acharya, G. Kane, S. Watson, and P. Kumar, A Non-thermal WIMP Miracle, Phys. Rev. D80, 083529 (2009), arXiv:0908.2430 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  10. [10]

    G. L. Kane, P. Kumar, B. D. Nelson, and B. Zheng, Dark matter production mechanisms with a nonthermal cosmological history: A classification, Phys. Rev. D93, 063527 (2016), arXiv:1502.05406 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  11. [11]

    Inflatable Dark Matter

    H. Davoudiasl, D. Hooper, and S. D. McDermott, Inflat- able Dark Matter, Phys. Rev. Lett.116, 031303 (2016), arXiv:1507.08660 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  12. [12]

    Flooded Dark Matter and S Level Rise

    L. Randall, J. Scholtz, and J. Unwin, Flooded Dark Mat- ter and S Level Rise, JHEP03, 011, arXiv:1509.08477 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  13. [13]

    R. T. Co, F. D’Eramo, L. J. Hall, and D. Pappadop- ulo, Freeze-In Dark Matter with Displaced Signatures at Colliders, JCAP12, 024, arXiv:1506.07532 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  14. [14]

    J. A. Dror, E. Kuflik, and W. H. Ng, Codecaying Dark Matter, Phys. Rev. Lett.117, 211801 (2016), arXiv:1607.03110 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  15. [15]

    Fingerprints of freeze-in dark matter in an early matter-dominated era

    A. Banerjee and D. Chowdhury, Fingerprints of freeze-in dark matter in an early matter-dominated era, SciPost Phys.13, 022 (2022), arXiv:2204.03670 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  16. [16]

    E. W. Kolb and M. S. Turner,The Early Universe, Vol. 69 (Taylor and Francis, 2019)

    work page 2019

  17. [17]

    Hamdan and J

    S. Hamdan and J. Unwin, Dark Matter Freeze-out Dur- ing Matter Domination, Mod. Phys. Lett. A33, 1850181 (2018), arXiv:1710.03758 [hep-ph]

    work page arXiv 2018

  18. [18]

    Chanda, S

    P. Chanda, S. Hamdan, and J. Unwin, RevivingZand Higgs Mediated Dark Matter Models in Matter Domi- nated Freeze-out, JCAP01, 034, arXiv:1911.02616 [hep- ph]

    work page arXiv 1911

  19. [19]

    Chanda and J

    P. Chanda and J. Unwin, Decoupling of asymmetric dark matter during an early matter dominated era, JCAP06, 032, arXiv:2102.02313 [hep-ph]

    work page arXiv

  20. [20]

    Steigman and M

    G. Steigman and M. S. Turner, Cosmological Constraints on the Properties of Weakly Interacting Massive Parti- cles, Nucl. Phys. B253, 375 (1985)

    work page 1985

  21. [21]

    Supersymmetric Dark Matter

    G. Jungman, M. Kamionkowski, and K. Griest, Super- symmetric dark matter, Phys. Rept.267, 195 (1996), arXiv:hep-ph/9506380

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  22. [22]

    Particle Dark Matter: Evidence, Candidates and Constraints

    G. Bertone, D. Hooper, and J. Silk, Particle dark matter: Evidence, candidates and constraints, Phys. Rept.405, 279 (2005), arXiv:hep-ph/0404175

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  23. [23]

    Precise Relic WIMP Abundance and its Impact on Searches for Dark Matter Annihilation

    G. Steigman, B. Dasgupta, and J. F. Beacom, Precise Relic WIMP Abundance and its Impact on Searches for Dark Matter Annihilation, Phys. Rev. D86, 023506 (2012), arXiv:1204.3622 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  24. [24]

    The Waning of the WIMP? A Review of Models, Searches, and Constraints

    G. Arcadi, M. Dutra, P. Ghosh, M. Lindner, Y. Mam- brini, M. Pierre, S. Profumo, and F. S. Queiroz, The waning of the WIMP? A review of models, searches, and constraints, Eur. Phys. J. C78, 203 (2018), arXiv:1703.07364 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  25. [25]

    W. L. Xu, C. Dvorkin, and A. Chael, Probing sub- GeV Dark Matter-Baryon Scattering with Cosmolog- ical Observables, Phys. Rev. D97, 103530 (2018), arXiv:1802.06788 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  26. [26]

    Making dark matter out of light: freeze-in from plasma effects

    C. Dvorkin, T. Lin, and K. Schutz, Making dark matter out of light: freeze-in from plasma effects, Phys. Rev. D 99, 115009 (2019), [Erratum: Phys.Rev.D 105, 119901 (2022)], arXiv:1902.08623 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  27. [27]

    J. H. Chang, R. Essig, and S. D. McDermott, Super- nova 1987A Constraints on Sub-GeV Dark Sectors, Mil- licharged Particles, the QCD Axion, and an Axion-like Particle, JHEP09, 051, arXiv:1803.00993 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  28. [28]

    Constraints on millicharged dark matter and axion-like particles from timing of radio waves

    A. Caputo, L. Sberna, M. Frias, D. Blas, P. Pani, L. Shao, and W. Yan, Constraints on millicharged dark matter and axionlike particles from timing of radio waves, Phys. Rev. D100, 063515 (2019), arXiv:1902.02695 [astro- ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  29. [29]

    E. Iles, S. Heeba, and K. Schutz, Dark Matter Di- rect Detection Experiments Are Sensitive to the Mil- licharged Background, Phys. Rev. Lett.134, 121002 (2025), arXiv:2407.21096 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  30. [30]

    I. B. Zel’dovich, Electromagnetic Interaction with Parity Violation, Sov. Phys. JETP6, 1184 (1958)

    work page 1958

  31. [31]

    Direct and indirect limits on the electro-magnetic form factors of WIMPs

    M. Pospelov and T. ter Veldhuis, Direct and indirect lim- its on the electromagnetic form-factors of WIMPs, Phys. Lett. B480, 181 (2000), arXiv:hep-ph/0003010

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  32. [32]

    Sigurdson, M

    K. Sigurdson, M. Doran, A. Kurylov, R. R. Caldwell, and M. Kamionkowski, Dark-matter electric and mag- netic dipole moments, Phys. Rev. D70, 083501 (2004), [Erratum: Phys.Rev.D 73, 089903 (2006)], arXiv:astro- ph/0406355

    work page arXiv 2004

  33. [33]

    Dipolar Dark Matter

    E. Masso, S. Mohanty, and S. Rao, Dipolar Dark Matter, Phys. Rev. D80, 036009 (2009), arXiv:0906.1979 [hep- ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  34. [34]

    Electromagnetic properties of dark matter: dipole moments and charge form factor

    V. Barger, W.-Y. Keung, and D. Marfatia, Electro- magnetic properties of dark matter: Dipole moments and charge form factor, Phys. Lett. B696, 74 (2011), arXiv:1007.4345 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  35. [35]

    C. M. Ho and R. J. Scherrer, Anapole Dark Matter, Phys. Lett. B722, 341 (2013), arXiv:1211.0503 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  36. [36]

    B. J. Kavanagh, P. Panci, and R. Ziegler, Faint Light from Dark Matter: Classifying and Constraining Dark Matter-Photon Effective Operators, JHEP04, 089, arXiv:1810.00033 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  37. [37]

    Dark matter electromagnetic dipoles: the WIMP expectation

    T. Hambye and X.-J. Xu, Dark matter electromag- 16 netic dipoles: the WIMP expectation, JHEP11, 156, arXiv:2106.01403 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  38. [38]

    Anapole Moment of Majorana Fermions and Implications for Direct Detection of Neutralino Dark Matter

    A. Ibarra, M. Reichard, and R. Nagai, Anapole mo- ment of Majorana fermions and implications for direct detection of neutralino dark matter, JHEP01, 086, arXiv:2207.01014 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  39. [39]

    E. E. Radescu, On the Electromagnetic Properties of Ma- jorana Fermions, Phys. Rev. D32, 1266 (1985)

    work page 1985

  40. [40]

    Direct Detection of Dark Matter Electromagnetic Dipole Moments

    T. Banks, J.-F. Fortin, and S. Thomas, Direct Detec- tion of Dark Matter Electromagnetic Dipole Moments, (2010), arXiv:1007.5515 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  41. [41]

    Direct detection of Light Anapole and Magnetic Dipole DM

    E. Del Nobile, G. B. Gelmini, P. Gondolo, and J.-H. Huh, Direct detection of Light Anapole and Magnetic Dipole DM, JCAP06, 002, arXiv:1401.4508 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  42. [42]

    D. Bose, D. Chowdhury, P. Mondal, and T. S. Ray, Trou- bles mounting for multipolar dark matter, JHEP06, 014, arXiv:2312.05131 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  43. [43]

    Probing Dark Matter Electromagnetic Properties in Direct Detection Experiments

    A. Ibarra, M. Reichard, and G. Tomar, Probing dark matter electromagnetic properties in direct detection ex- periments, JCAP02, 072, arXiv:2408.15760 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  44. [44]

    Kumar, B

    J. Kumar, B. Mondal, G. Muralidhara, and N. Raj, Di- rect detection of electromagnetically interacting ultra- heavy dark matter, (2025), arXiv:2509.24938 [hep-ph]

    work page arXiv 2025

  45. [45]

    Effect of electromagnetic dipole dark matter on energy transport in the solar interior

    B. Geytenbeek, S. Rao, P. Scott, A. Serenelli, A. C. Vin- cent, M. White, and A. G. Williams, Effect of electro- magnetic dipole dark matter on energy transport in the solar interior, JCAP03, 029, arXiv:1610.06737 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  46. [46]

    Constraints on electromagnetic form factors of sub-GeV dark matter from the Cosmic Microwave Background anisotropy

    G. Lambiase, S. Mohanty, A. Nautiyal, and S. Rao, Constraints on electromagnetic form factors of sub- GeV dark matter from the cosmic microwave back- ground anisotropy, Phys. Rev. D104, 023519 (2021), arXiv:2102.04840 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  47. [47]

    Collider Constraints on Dipole-Interacting Dark Matter

    J.-F. Fortin and T. M. P. Tait, Collider Constraints on Dipole-Interacting Dark Matter, Phys. Rev. D85, 063506 (2012), arXiv:1103.3289 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  48. [48]

    X. Chu, J. Pradler, and L. Semmelrock, Light dark states with electromagnetic form factors, Phys. Rev. D99, 015040 (2019), arXiv:1811.04095 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  49. [49]

    R. J. Scherrer and M. S. Turner, Decaying particles do not “heat up” the Universe, Phys. Rev. D31, 681 (1985)

    work page 1985

  50. [50]

    Deflationary Universe Scenario

    B. Spokoiny, Deflationary universe scenario, Phys. Lett. B315, 40 (1993), arXiv:gr-qc/9306008

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  51. [51]

    M. L. Graesser, I. M. Shoemaker, and L. Vec- chi, Asymmetric WIMP dark matter, JHEP10, 110, arXiv:1103.2771 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  52. [52]

    R. J. Scherrer and M. S. Turner, On the Relic, Cos- mic Abundance of Stable Weakly Interacting Massive Particles, Phys. Rev. D33, 1585 (1986), [Erratum: Phys.Rev.D 34, 3263 (1986)]

    work page 1986

  53. [53]

    Appendiciario -- A hands-on manual on the theory of direct Dark Matter detection

    E. Del Nobile, The Theory of Direct Dark Matter De- tection: A Guide to Computations 10.1007/978-3-030- 95228-0 (2021), arXiv:2104.12785 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/978-3-030- 2021

  54. [54]

    Y. Gao, C. M. Ho, and R. J. Scherrer, Anapole Dark Matter at the LHC, Phys. Rev. D89, 045006 (2014), arXiv:1311.5630 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  55. [55]

    Light and Darkness: consistently coupling dark matter to photons via effective operators

    C. Arina, A. Cheek, K. Mimasu, and L. Pagani, Light and Darkness: consistently coupling dark matter to photons via effective operators, Eur. Phys. J. C81, 223 (2021), arXiv:2005.12789 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  56. [56]

    S. Y. Choi, J. Jeong, D. W. Kang, and S. Shin, Hunting for hypercharge anapole dark matter in all spin scenarios, Phys. Rev. D109, 096001 (2024), arXiv:2401.02855 [hep- ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  57. [57]

    PandaX Collaboration, Limits on the luminance of dark matter from xenon recoil data, Nature618, 47 (2023)

    work page 2023

  58. [58]

    A systematic investigation on dark matter-electron scattering in effective field theories

    J.-H. Liang, Y. Liao, X.-D. Ma, and H.-L. Wang, A systematic investigation on dark matter-electron scattering in effective field theories, JHEP07, 279, arXiv:2406.10912 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  59. [59]

    Dark matter in the Sun: scattering off electrons vs nucleons

    R. Garani and S. Palomares-Ruiz, Dark matter in the Sun: scattering off electrons vs nucleons, JCAP05, 007, arXiv:1702.02768 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  60. [60]

    Evaporation and scattering of momentum- and velocity-dependent dark matter in the Sun

    G. Busoni, A. De Simone, P. Scott, and A. C. Vin- cent, Evaporation and scattering of momentum- and velocity-dependent dark matter in the Sun, JCAP10, 037, arXiv:1703.07784 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  61. [61]

    Impact of galactic distributions in celestial capture of dark matter

    D. Bose and S. Sarkar, Impact of galactic distributions in celestial capture of dark matter, Phys. Rev. D107, 063010 (2023), arXiv:2211.16982 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  62. [62]

    A new Generation of Standard Solar Models

    N. Vinyoles, A. M. Serenelli, F. L. Villante, S. Basu, J. Bergstr¨ om, M. C. Gonzalez-Garcia, M. Maltoni, C. Pe˜ na-Garay, and N. Song, A new Generation of Standard Solar Models, Astrophys. J.835, 202 (2017), arXiv:1611.09867 [astro-ph.SR]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  63. [63]

    R. H. Helm, Inelastic and Elastic Scattering of 187-Mev Electrons from Selected Even-Even Nuclei, Phys. Rev. 104, 1466 (1956)

    work page 1956

  64. [64]

    The leptophilic dark matter in the Sun: the minimum testable mass

    Z.-L. Liang, Y.-L. Tang, and Z.-Q. Yang, The leptophilic dark matter in the Sun: the minimum testable mass, JCAP10, 035, arXiv:1802.01005 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  65. [65]

    Evaporation of dark matter from celestial bodies

    R. Garani and S. Palomares-Ruiz, Evaporation of dark matter from celestial bodies, JCAP05(05), 042, arXiv:2104.12757 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  66. [66]

    Q. Liu, J. Lazar, C. A. Arg¨ uelles, and A. Kheirandish, χaroν: a tool for neutrino flux generation from WIMPs, JCAP10, 043, arXiv:2007.15010 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  67. [67]

    C. A. Arg¨ uelles, J. Salvado, and C. N. Weaver, nuSQuIDS: A toolbox for neutrino propagation, Comput. Phys. Commun.277, 108346 (2022), arXiv:2112.13804 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  68. [68]

    T. N. Maity, A. K. Saha, S. Mondal, and R. Laha, Neutrinos from the Sun can discover dark matter- electron scattering, Phys. Rev. D112, 023025 (2025), arXiv:2308.12336 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  69. [69]

    M. G. Aartsenet al.(IceCube), Search for annihilating dark matter in the Sun with 3 years of IceCube data, Eur. Phys. J. C77, 146 (2017), [Erratum: Eur.Phys.J.C 79, 214 (2019)], arXiv:1612.05949 [astro-ph.HE]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  70. [70]

    Abbasiet al.(IceCube), Search for GeV-scale dark matter annihilation in the Sun with IceCube DeepCore, Phys

    R. Abbasiet al.(IceCube), Search for GeV-scale dark matter annihilation in the Sun with IceCube DeepCore, Phys. Rev. D105, 062004 (2022), arXiv:2111.09970 [astro-ph.HE]

    work page arXiv 2022

  71. [71]

    Planck 2018 results. VI. Cosmological parameters

    N. Aghanimet al.(Planck), Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys.641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  72. [72]

    Model-independent WIMP Scattering Responses and Event Rates: A Mathematica Package for Experimental Analysis

    N. Anand, A. L. Fitzpatrick, and W. C. Haxton, Weakly interacting massive particle-nucleus elastic scattering re- sponse, Phys. Rev. C89, 065501 (2014), arXiv:1308.6288 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  73. [73]

    J. C. Criado, A. Djouadi, M. Perez-Victoria, and J. San- tiago, A complete effective field theory for dark matter, JHEP07, 081, arXiv:2104.14443 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv

  74. [74]

    Neutron stars as thermometers for reheating induced dipole dark matter

    S. Jahedi, Neutron stars as thermometers for reheating induced dipole dark matter, (2026), arXiv:2607.01390 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2026