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REVIEW 5 major objections 5 minor 104 references

Can Q-balls describe cosmological and galactic dark matter?

T0 review · 5 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Millicharged Q-balls formed in the early universe can act as cold dark matter cosmologically and, once condensed into a superfluid, mimic MOND in galaxies, giving both paradigms one origin.

desk verdict The central claim doesn't hold up: inconsistent Q-ball scalings and a leftover-field overclosure problem undermine the paper, though the proposed CDM+MOND unification idea is new and worth a look. read the letter →

arxiv 2502.00821 v1 pith:W5BUWSEI submitted 2025-02-02 hep-th astro-ph.COgr-qchep-ph

Susobhan Mandal , S. Shankaranarayanan (IIT Bombay) This is my paper · ORCID
classification hep-thastro-ph.COgr-qchep-ph
keywords Q-ballsdarkmatterMONDsuperfluidBose-Einsteincondensatemillichargedparticlesradiation-dominatedepochcomplexscalarfield
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

This paper argues that the same object, a non-topological soliton called a Q-ball, can supply the dark matter at both cosmological and galactic scales. It shows that millicharged composite Q-balls can form from a complex scalar field during the radiation-dominated epoch, decay in energy density as $1/a^3$, and therefore behave as cold dark matter. In the late universe, it argues, these Q-balls condense into a Bose-Einstein condensate and a superfluid whose phonons produce a MOND-like force law. If the scenario is right, CDM and MOND are not competing explanations but two phases of a single Q-ball fluid.

What carries the argument

The load-bearing object is the thin-wall Q-ball solution of a complex scalar field with polynomial potential $\bar{U}(\sigma) = \frac{1}{2}m_\sigma^2 a^2\sigma^2 - \frac{\zeta}{4}\sigma^4 + \frac{\xi}{6a^2}\sigma^6$. The paper shows that such Q-balls exist in the radiation-dominated epoch when the inequality $a^2(m_\sigma^2 - 3\zeta^2/16\xi) < \lambda^2 < (m_\sigma a)^2$ holds, and that they are classically stable in the thin-wall limit. The mechanism that produces CDM behavior is the scaling $\rho_Q \sim 1/a^3$ in the radiation-dominated epoch. The mechanism that produces MOND is the phonon effective Lagrangian obtained after integrating out the massive radial mode; in the infrared limit $\zeta \to 0$ it takes the form $L_\pi \sim (2/3\sqrt{\xi})X\sqrt{X}$, the $X^{3/2}$ phonon structure that yields a MOND-like force on baryons.

What would settle it

Compute the relic abundance of the free scalar field using the paper's number-density expressions (44)-(56) with $m_\sigma \sim 10$-$30\,\mathrm{keV}$ and the Q-ball abundance needed for dark matter. If the leftover-particle energy density exceeds the observed dark matter density unless an unspecified depletion mechanism is added, the scenario is falsified; this calculation uses only expressions already in the paper.

Watch

Extended reading notes

Core claim

The paper's central claim is that Q-balls, localized non-topological solitons held together by conserved global U(1) charge, provide one dark-matter candidate that behaves as CDM at cosmological scales and produces MOND-like behavior at galactic scales. The authors derive conditions for Q-ball formation in the radiation-dominated epoch and, from matter-radiation equality, fix the Q-ball mass to about $1\,\mathrm{eV}$, much lighter than the electron. They combine this with the invisible-decay bound of ortho-positronium to obtain a millicharge limit $Q < 3.4 \times 10^{-5}$. They then show that the Q-ball energy density redshifts as $1/a^3$, like pressureless matter, and that in the present universe the Q-balls form a Bose-Einstein condensate and a superfluid; the low-energy phonon action reduces to an $X^{3/2}$ structure, which yields MOND behavior at galactic scales. Thus the same fluid is claimed to explain structure formation on large scales and flat rotation curves on small scales.

Load-bearing premise

The load-bearing premise is that the free scalar particles left over after Q-ball formation have a negligible cosmological abundance; the paper's own estimate leaves roughly a million free particles for every Q-ball, and since those particles are far heavier than the Q-balls, any surviving population would swamp the dark matter density.

Editorial extensions

If this is right

  • If the paper is right, dark matter on galactic scales is a collective superfluid rather than a collection of collisionless particles, so halo density profiles and satellite abundances would be modified in the inner regions.
  • The model predicts Q-balls with mass near $1\,\mathrm{eV}$ and millicharge $Q < 3.4 \times 10^{-5}$, which can be tested through invisible decays of ortho-positronium and other millicharged-particle searches.
  • The transition $\rho_Q \sim 1/a^3$ means Q-balls dominate at matter-radiation equality and seed structure formation in the same way as CDM, preserving the large-scale success of the cosmological model.
  • The superfluid sound speed $c_s = \sqrt{g\rho}/(2m^2)$ sets a threshold: mergers below this speed pass through with little friction and take longer than in CDM, while faster mergers behave like CDM, a distinction visible in galaxy merger statistics.

Reading between the lines

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

  • If the leftover scalar field is not removed, the paper's own estimate $n_Q/n_\Phi \sim 10^{-6}$ implies the free particles dominate the energy budget; computing the relic abundance of $\Phi$ is the first decisive test of the scenario.
  • One could look for a small-scale signature in dwarf-galaxy rotation curves: the phonon-mediated force should produce a characteristic core or flattening that collisionless CDM would not produce at the same radius.
  • The framework suggests a concrete relation between the dark-matter superfluid sound speed and the MOND acceleration scale $a_0$; measuring both in the same galaxy would test whether the phonon mediator is the right mechanism.
  • The model's viability depends on a primordial U(1) charge asymmetry, so mapping the predicted Q-ball abundance onto magnetogenesis or gravitational-wave helicity sources would sharpen the allowed parameter space.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 5 minor

Summary. The manuscript proposes a unified dark-matter model in which millicharged composite Q-balls, formed from a complex scalar with a φ^6-stabilized potential during the radiation-dominated epoch, behave as cold dark matter at cosmological scales (ρ_Q ∼ a^-3) and later condense into a superfluid whose phonon effective action has the X^(3/2) structure of the Berezhiani–Khoury model, thereby reproducing MOND-like behavior at galactic scales. Sections II and III derive Q-ball existence and stability conditions with thermal corrections, compute formation rates and number densities, and use matter–radiation equality to obtain a Q-ball mass M_Q ≈ 1 eV and an ortho-positronium bound Q < 3.4×10^-5. Section IV constructs the BEC and superfluid phases and derives the low-energy phonon action. The paper concludes that CDM and MOND are different phases of the same Q-ball fluid.

Significance. The proposed unification is conceptually interesting, and the paper contains useful explicit constructions: the FRW Q-ball equations, the thermal effective potential, the thin-wall solution, and the derivation of L_pert ∼ X^(3/2) from a φ^6-type potential. If the central claims were sound, the model would be a significant step toward a common origin for CDM and MOND. However, the cosmological core of the paper is not internally consistent: the energy-density scaling differs by a factor a^(3/2) between two key equations, and the predicted abundance of residual Φ particles overcloses the universe by many orders of magnitude. The manuscript therefore does not, in its present form, establish the claimed cosmological behavior.

major comments (5)
  1. [Appendix B / §III.B / §V] Eq. (B14) states ρ_Q ∼ a^-3, which is the CDM-like behavior used in §III and the abstract, but Eq. (58) and Eq. (103) give ρ_Q ∼ a^-3/2 (with an additional factor e^(aQΔ/T0) in Eq. (58) that is then dropped). The a^-3/2 scaling is used in the matter–radiation equality calculation, Eqs. (59)–(61), and in the Friedmann discussion, Eq. (103), where it yields H_MD ∼ H_0(1+z)^(3/4), which is explicitly not the CDM expansion. These two scalings cannot both be correct, and the manuscript never reconciles them. Since the CDM claim depends on Eq. (B14) while the mass and equality results depend on Eq. (58), this contradiction undermines both the cosmological behavior and the derived M_Q ≈ 1 eV.
  2. [§III.A, Eq. (56)] Eq. (56) gives n_Q/n_Φ ∼ 10^-6, and the text notes that the Φ number density is about 10^6 times larger than the Q-ball number density. With m_σ ∼ 10–30 keV and M_Q ≈ 1 eV, the free-Φ energy density exceeds the Q-ball energy density by ρ_Φ/ρ_Q ∼ (m_σ/M_Q)(n_Φ/n_Q) ∼ 10^10–10^11. No depletion mechanism for the leftover Φ population is provided; since Eq. (56) is derived after solitosynthesis and Q-ball formation, the same charge-accumulation process cannot remove this population without also destroying the Q-balls. Consequently, the universe would be dominated by Φ particles long before the proposed equality of Eqs. (59)–(61), and the assumption that Q-balls drive the RD-to-MD transition is not viable.
  3. [§II.B, Eq. (40)] Eq. (40) is dimensionally inconsistent: the left side of the implication Q^-1 = m_σ sqrt(1 − 3ζ²/(16 ξ̄)) > 3×10^4 eV has Q^-1 dimensionless while the right side has units of energy. Relatedly, the symbol Q denotes both the dimensionless global U(1) charge in E_λ = λQ and the electric millicharge constrained by ortho-positronium (Q < 3.4×10^-5); these are different quantities. The claimed lower bound m_σ > 30 keV therefore does not follow from the stated equations, and the subsequent parameter constraints based on it are not established.
  4. [§IV.D, Eqs. (98)–(102)] The galactic-scale MOND claim rests on Eq. (102), L_pert ∼ (2/(3√ξ)) X√X, which is obtained from Eq. (98) only for ζ ≪ ξ m² and for X > 0. The paper asserts X > 0 because the phonon action should be real and positive, but this is an assumption about the galactic regime rather than a derivation, and the limit σ_0 → 0 is asserted from ζ → 0 without specifying a controlled IR flow for both ζ and ξ (ξ is described as irrelevant, so its value at galaxy scales is not fixed). Moreover, the paper stops at the phonon action; it does not derive the coupling of phonons to baryons or the MOND acceleration a_0, so the identification with the Berezhiani–Khoury MOND mechanism is imported rather than demonstrated.
  5. [§III.B, Eq. (61)] The derivation of M_Q ≈ 1 eV fixes z_eq = 3600 and imposes ρ_Q = ρ_rad, i.e. it assumes that Q-balls are the dominant matter component driving equality. In addition, Eq. (58) contains a factor e^(aQΔ/T0) > 1 that is omitted in Eq. (59), and Eq. (61) is labelled an upper limit but is then used as the central mass prediction. Thus the quoted mass is a consistency constraint with an input assumption, not an independent prediction, and it inherits the incorrect a^-3/2 scaling noted above.
minor comments (5)
  1. [§III.A, Eq. (47)] The ratio in Eq. (47) is written n_Q/n_Q^Φ; this should be n_Q/n_Φ. The same notation issue appears in the surrounding text and should be corrected throughout.
  2. [§II.A] The sentence ending 'Appendix B shows that, in the thin-wall approximation, the Q-ball approximation has more energy' is unclear and appears to contradict the stability discussion; the authors should rewrite this passage to state what is being compared.
  3. [General notation] The symbol Q is used for the global U(1) charge, the electric millicharge, and as shorthand for a Q-ball state in Eq. (39); this triple meaning makes Sections II and III unnecessarily difficult to follow, especially in Eq. (40) and the ortho-positronium constraint.
  4. [§III.B, Eq. (61)] The numerical value 2.6/g_Q^(2/5) eV should be accompanied by the explicit assumptions for g_Q and z_eq in the main text; currently the reader must reconstruct them from Eq. (59).
  5. [§V, Eq. (103)] Eq. (103) follows directly from Eq. (58); if the a^-3/2 scaling is retained, the contradiction with Eq. (B14) should be addressed in this section rather than presented as a new result.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Q-ball mass is fixed by an explicitly stated consistency condition, and the MOND-like phonon action is derived from the model's own potential rather than imported.

full rationale

The central derivation chain is largely self-contained. In Sec. III.B, the Q-ball mass is obtained by equating the Q-ball energy density of Eq. (58) to the radiation energy density at z_eq = 3600; the paper explicitly frames this as imposing a constraint ('by viewing Q-matter as a potential candidate for dark matter and requiring the equality of radiation and matter at a redshift of z = 3600, it is possible to impose constraints on either the values of charge Q and lambda_0 or the mass E_Q'). This is transparent parameter fixing, not a hidden fit or a renamed prediction, and the resulting mass is then used for an independent BEC check (m <= 15 eV condition). The MOND/superfluid claim is also not circular: Eqs. (94)-(102) derive L_pert ~ X^(3/2) from the model's own zeta/2 |Phi|^4 - xi/3 |Phi|^6 potential, with the Berezhiani-Khoury work cited only to identify the resulting structure as the MOND-type action, not as the source of the derivation. The self-citations ([64, 89, 90, 102]) supply an input charge-asymmetry mechanism and a decoupling check, but neither functions as an imported uniqueness theorem nor as the target result. The paper does contain serious non-circular problems: Eq. (56) gives n_Q/n_Phi ~ 10^-6, which together with m_sigma >> M_Q implies that the leftover Phi field would dominate the energy budget, contrary to the paper's viability conclusion; and rho_Q ~ a^-3 (Eq. B14) is inconsistent with rho_Q ~ a^-3/2 (Eqs. 58 and 103). These are correctness risks, not circularity, and should be assessed as such.

Assumptions & free parameters 6 free parameters · 7 assumptions · 2 invented entities

The model introduces a new dark scalar sector with a specific potential and several unconstrained couplings (m_sigma, zeta, xi, Q, eta_Q, g_Q). The cosmological abundance and the MOND behavior both depend on these free parameters. The thin-wall approximation, the decoupling from photons, the primordial charge asymmetry, and the transfer of the Berezhiani-Khoury superfluid mechanism are all assumed rather than derived from independent evidence.

free parameters (6)
  • m_sigma = 10 to 30 keV
    Chosen so that the dimensionless critical temperature T_bar_c ~ 1 corresponds to the recombination-era energy scale and to satisfy the ortho-positronium bound (Eq. 40); it sets the Q-ball mass scale.
  • zeta (quartic coupling) = negative; illustrative values -0.1 and -1e-9
    Sets the attractive potential needed for Q-ball formation; constrained only by zeta^2 <= 16 xi_bar/3 (Eq. 26). Its value changes the Q-ball profile and the low-energy phonon action.
  • xi (hexic coupling) = illustrative values 0.01 and 1e-6
    Stabilizes the potential and controls the Q-ball radius and the strength of the phonon action; no independent measurement is provided.
  • Q (charge / millicharge) = < 3.4e-5 from ortho-positronium bound
    Labeled as the Q-ball charge but used as the millicharge parameter in the abstract and Eq. (40). The integer-charge interpretation required by solitosynthesis is not reconciled with this small bound.
  • eta_Q (charge asymmetry) = unspecified; argued to arise from helical magnetic fields
    Sets the overall Q-ball number density through Eqs. (36)-(38) and Eq. (54). No observational input or direct calculation is provided.
  • g_Q (internal partition function) = assumed O(1) in Eq. (61)
    Enters the Q-ball abundance and the derived mass limit; its value is not computed from microphysics.
assumptions (7)
  • standard math Standard Q-ball existence and stability conditions from Ref. [80] are valid in the RD epoch.
    Invoked in Eqs. (21)-(25) and Appendix C to guarantee Q-ball formation and stability.
  • domain assumption The thin-wall approximation for large Q-balls is valid in the RD and MD epochs.
    Appendix B uses sigma(r) = sigma0 Theta(R-r); the entire mass and radius derivation depends on this approximation.
  • domain assumption The background U(1) gauge field vanishes in FRW, so Q-balls decouple from photons.
    Appendix A shows tree-level decoupling, but the full non-linear plasma behavior is not analyzed; this decoupling is required for Q-balls to act as CDM.
  • domain assumption A primordial U(1) charge asymmetry eta_Q exists and the chemical potential mu_Phi is of order m_sigma.
    Eqs. (35)-(38) and the discussion after Eq. (58) require this for Q-ball formation and for the number density estimates.
  • domain assumption The Berezhiani-Khoury superfluid dark matter mechanism applies to the Q-ball condensate.
    Section IV.D borrows the X^{3/2} phonon effective action from Ref. [69] and assumes that phonon-mediated forces reproduce MOND.
  • ad hoc to paper The phonon effective action is real and positive, so X > 0 in the galactic regime.
    Eq. (102) requires X > 0 for the X^{3/2} action; the paper justifies this by asserting that the (gradient pi)^2 term is small and sigma0 tends to zero, rather than deriving it.
  • standard math Derrick's theorem and classical stability conditions apply to the time-dependent FRW background.
    Appendix C uses these conditions to argue that the Q-balls are stable during the RD epoch.
invented entities (2)
  • Dark complex scalar field Phi
    purpose: Constituent field for Q-balls; carries global U(1) charge and millicharge; forms the dark matter superfluid.
    The paper postulates this field with a non-renormalizable hexic potential and negative quartic coupling; there is no direct evidence, and the only external handle is the ortho-positronium bound applied to its composite Q-balls.
  • Millicharged composite Q-balls
    purpose: Dark matter candidate that acts as CDM cosmologically and as a superfluid phonon fluid on galactic scales.
    Q-balls are known solitons, but the specific dark-sector millicharged realization is new; no unique observable signature is computed that would distinguish it from other dark matter models.

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Pith. "Pith review of Can Q-balls describe cosmological and galactic dark matter?." pith.science (2026). https://pith.science/paper/W5BUWSEI

@misc{pith2026250200821,
  author       = {Pith},
  title        = {Pith review of: Can Q-balls describe cosmological and galactic dark matter?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W5BUWSEI}},
  note         = {Machine review of arXiv:2502.00821}
}
abstract

The Cold Dark Matter (CDM) hypothesis accurately predicts large-scale structure formation and fits the Cosmic Microwave Background temperature fluctuations (CMB). However, observations of the inner regions of dark matter halos and dwarf galaxy satellites have consistently posed challenges to CDM. On the other hand, the Modified Newtonian Dynamics (MOND) hypothesis can explain galactic phenomena but fails to account for the complex shape of the CMB and matter power spectra. CDM and MOND are effective in nearly mutually exclusive regimes, prompting the question: Is there a physical mechanism where CDM and MOND share a common origin? Q-balls, which are localized, non-topological solitons, can be a bridge between the two hypotheses. Q-balls formed in the early Universe can mimic CDM at cosmological scales. Interestingly, Q-balls can exhibit MOND-like behavior in the late Universe at galactic scales, providing a unified framework. Specifically, we demonstrate that millicharged composite Q-balls formed from complex scalar fields, decoupled from the background radiation, can naturally arise during the radiation-dominated epoch. From the matter-radiation equality, we also obtain the mass of Q-balls to be $1~{eV}$, which are much smaller than the electron mass. Using the constraints from the invisible decay mode of ortho-positronium, we obtain $Q < 3.4 \times 10^{-5}$. We also establish an upper bound on the number density of Q-balls, which depends on the charge of the Q-ball and the small initial charge asymmetry. Furthermore, we demonstrate that the MOND naturally emerges at the galactic scale within the framework of our Q-ball model.

Figures

Figures reproduced from arXiv: 2502.00821 by the authors.

Figure 1
Figure 1. FIG. 1. Plot of effective field potential for three different temperatures ( [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. plot of effective field potential for three different (scaled) temperatures ( [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗

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Works this paper leans on

104 extracted references · 65 canonical work pages

  1. [1]

    (99) As a result of the relation mentioned above, we obtain the following expression of Lpert Lpert = ζ 3 + 12ζξX + (ζ 2 + 4ξX )3/2 12ξ2 . (100) We know from renormalization group flow [97] of ϕ4-theory that ζ(p) = ζ(m) 1 − 3ζ(m) 16π2 log p m , (101) 29 which means in the IR limit (galaxy scale) ζ → 0 and this conclusion is valid even after the inclusion ...

  2. [2]

    A. R. Liddle and D. H. Lyth, Physics Reports 231, 1 (1993)

    1993

  3. [3]

    J. F. Navarro, in Symposium-international astronomical union, Vol. 171 (Cambridge Univer- sity Press, 1996) pp. 255–258

    1996

  4. [4]

    Dubinski and R

    J. Dubinski and R. Carlberg, The Astrophysical Journal 378, 496 (1991)

    1991

  5. [5]

    Diemand and B

    J. Diemand and B. Moore, Advanced Science Letters 4, 297 (2011)

    2011

  6. [6]

    Silk and A

    J. Silk and A. Stebbins, Astrophysical Journal-Part 1 (ISSN 0004-637X), vol. 411, no. 2, p. 439-449. 411, 439 (1993)

    1993

  7. [7]

    Klypin, A

    A. Klypin, A. V. Kravtsov, J. S. Bullock, and J. R. Primack, The Astrophysical Journal 554, 903 (2001)

    2001

  8. [8]

    Bertone, ed., Particle Dark Matter: Observations, Models and Searches (Cambridge Univ

    G. Bertone, ed., Particle Dark Matter: Observations, Models and Searches (Cambridge Univ. Press, Cambridge, 2010)

    2010

Show all 104 references
  1. [9]

    A. A. Prinz et al. , Phys. Rev. Lett. 81, 1175 (1998), arXiv:hep-ex/9804008

    1998 arXiv

  2. [10]

    de Montigny, P.-P

    M. de Montigny, P.-P. A. Ouimet, J. Pinfold, A. Shaa, and M. Staelens, (2023), arXiv:2307.07855 [hep-ph]

    2023 arXiv

  3. [11]

    Kusenko and P

    A. Kusenko and P. J. Steinhardt, Physical review letters 87, 141301 (2001)

    2001

  4. [12]

    D. N. Spergel and P. J. Steinhardt, Physical review letters 84, 3760 (2000)

    2000

  5. [13]

    B. D. Wandelt, R. Dave, G. R. Farrar, P. C. McGuire, D. N. Spergel, and P. J. Steinhardt, in Sources and Detection of Dark Matter and Dark Energy in the Universe: Fourth International Symposium Held at Marina del Rey, CA, USA February 23–25, 2000 (Springer, 2001) pp. 263–274. 41

    2000

  6. [14]

    Willman, M

    B. Willman, M. R. Blanton, A. A. West, J. J. Dalcanton, D. W. Hogg, D. P. Schneider, N. Wherry, B. Yanny, and J. Brinkmann, The Astronomical Journal 129, 2692 (2005)

    2005

  7. [15]

    Belokurov, D

    V. Belokurov, D. B. Zucker, N. Evans, J. T. Kleyna, S. Koposov, S. Hodgkin, M. Irwin, G. Gilmore, M. Wilkinson, M. Fellhauer, et al., The Astrophysical Journal 654, 897 (2007)

    2007

  8. [16]

    Walsh, B

    S. Walsh, B. Willman, and H. Jerjen, The Astronomical Journal 137, 450 (2008)

    2008

  9. [17]

    Klypin, A

    A. Klypin, A. V. Kravtsov, O. Valenzuela, and F. Prada, The Astrophysical Journal 522, 82 (1999)

    1999

  10. [18]

    Moore, S

    B. Moore, S. Ghigna, F. Governato, G. Lake, T. Quinn, J. Stadel, and P. Tozzi, The Astro- physical Journal 524, L19 (1999)

    1999

  11. [19]

    Chae, Astrophys

    K.-H. Chae, Astrophys. J. 952, 128 (2023), arXiv:2305.04613 [astro-ph.GA]

    2023 arXiv

  12. [20]

    Nguyen, D

    N.-M. Nguyen, D. Huterer, and Y. Wen, Phys. Rev. Lett. 131, 111001 (2023)

    2023

  13. [21]

    F. J. Petriello and K. M. Zurek, Journal of High Energy Physics 2008, 047 (2008)

    2008

  14. [22]

    Steigman, B

    G. Steigman, B. Dasgupta, and J. F. Beacom, Physical Review D 86, 023506 (2012)

    2012

  15. [23]

    Roszkowski, E

    L. Roszkowski, E. M. Sessolo, and S. Trojanowski, Reports on Progress in Physics 81, 066201 (2018)

    2018

  16. [24]

    Schumann, Journal of Physics G: Nuclear and Particle Physics 46, 103003 (2019)

    M. Schumann, Journal of Physics G: Nuclear and Particle Physics 46, 103003 (2019)

    2019

  17. [25]

    L. D. Duffy and K. Van Bibber, New Journal of Physics 11, 105008 (2009)

    2009

  18. [26]

    Sikivie, International Journal of Modern Physics A 25, 554 (2010)

    P. Sikivie, International Journal of Modern Physics A 25, 554 (2010)

    2010

  19. [27]

    Visinelli and P

    L. Visinelli and P. Gondolo, Physical Review D 80, 035024 (2009)

    2009

  20. [28]

    Holman, G

    R. Holman, G. Lazarides, and Q. Shafi, Physical Review D 27, 995 (1983)

    1983

  21. [29]

    D. J. Marsh and J. Silk, Monthly Notices of the Royal Astronomical Society437, 2652 (2014)

    2014

  22. [30]

    V. B. Klaer and G. D. Moore, Journal of Cosmology and Astroparticle Physics 2017 (11), 049

    2017

  23. [31]

    Milgrom, Astrophysical Journal, Part 1 (ISSN 0004-637X), vol

    M. Milgrom, Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 270, July 15, 1983, p. 365-

    1983

  24. [32]

    Skordis and T

    C. Skordis and T. Zlo´ snik, Phys. Rev. Lett. 127, 161302 (2021)

    2021

  25. [33]

    Milgrom, The Astrophysical Journal 270, 371 (1983)

    M. Milgrom, The Astrophysical Journal 270, 371 (1983)

    1983

  26. [34]

    S. S. McGaugh, J. M. Schombert, G. D. Bothun, and W. De Blok, The Astrophysical Journal 533, L99 (2000). 42

    2000

  27. [35]

    R. H. Sanders and S. S. McGaugh, Annual Review of Astronomy and Astrophysics 40, 263 (2002)

    2002

  28. [36]

    Nipoti, P

    C. Nipoti, P. Londrillo, and L. Ciotti, Monthly Notices of the Royal Astronomical Society: Letters 381, L104 (2007)

    2007

  29. [37]

    S. S. McGaugh, The Astrophysical Journal 632, 859 (2005)

    2005

  30. [38]

    G. W. Angus, H. Y. Shan, H. S. Zhao, and B. Famaey, The Astrophysical Journal 654, L13 (2006)

    2006

  31. [39]

    G. W. Angus and A. Diaferio, Monthly Notices of the Royal Astronomical Society 417, 941 (2011)

    2011

  32. [40]

    Aguirre, J

    A. Aguirre, J. Schaye, and E. Quataert, The Astrophysical Journal 561, 550 (2001)

    2001

  33. [41]

    Sanders, Monthly Notices of the Royal Astronomical Society 342, 901 (2003)

    R. Sanders, Monthly Notices of the Royal Astronomical Society 342, 901 (2003)

    2003

  34. [42]

    Belotsky, A

    K. Belotsky, A. Dmitriev, E. Esipova, V. Gani, A. Grobov, M. Y. Khlopov, A. Kirillov, S. Rubin, and I. Svadkovsky, Modern Physics Letters A 29, 1440005 (2014)

    2014

  35. [43]

    P. H. Frampton, M. Kawasaki, F. Takahashi, and T. T. Yanagida, Journal of Cosmology and Astroparticle Physics 2010 (04), 023

    2010

  36. [44]

    ¨Ozsoy and G

    O. ¨Ozsoy and G. Tasinato, Universe 9, 203 (2023)

    2023

  37. [45]

    Clesse and J

    S. Clesse and J. Garc ´ ıa-Bellido, Physics of the Dark Universe22, 137 (2018)

    2018

  38. [46]

    Garc ´ ıa-Bellido, Handbook of Gravitational Wave Astronomy , 1 (2020)

    J. Garc ´ ıa-Bellido, Handbook of Gravitational Wave Astronomy , 1 (2020)

    2020

  39. [47]

    J. C. Niemeyer and K. Jedamzik, Physical Review D 59, 124013 (1999)

    1999

  40. [48]

    B. Carr, F. K¨ uhnel, and M. Sandstad, Physical Review D 94, 083504 (2016)

    2016

  41. [49]

    B. Carr, K. Kohri, Y. Sendouda, and J. Yokoyama, Reports on Progress in Physics 84, 116902 (2021)

    2021

  42. [50]

    Villanueva-Domingo, O

    P. Villanueva-Domingo, O. Mena, and S. Palomares-Ruiz, Frontiers in Astronomy and Space Sciences 8, 681084 (2021)

    2021

  43. [51]

    Sasaki, T

    M. Sasaki, T. Suyama, T. Tanaka, and S. Yokoyama, Classical and Quantum Gravity 35, 063001 (2018)

    2018

  44. [52]

    Lloyd-Stubbs and J

    A. Lloyd-Stubbs and J. McDonald, Physical Review D 105, 103532 (2022)

    2022

  45. [53]

    Carr and F

    B. Carr and F. K¨ uhnel, Annual Review of Nuclear and Particle Science 70, 355 (2020)

    2020

  46. [54]

    Coleman, Nuclear Physics B 262, 263 (1985)

    S. Coleman, Nuclear Physics B 262, 263 (1985)

    1985

  47. [55]

    Kusenko, Physics Letters B 404, 285 (1997)

    A. Kusenko, Physics Letters B 404, 285 (1997)

    1997

  48. [56]

    Kusenko and M

    A. Kusenko and M. Shaposhnikov, Physics Letters B 418, 46 (1998)

    1998

  49. [57]

    Cohen, S

    A. Cohen, S. Coleman, H. Georgi, and A. Manohar, Nuclear Physics B 272, 301 (1986)

    1986

  50. [58]

    Anagnostopoulos, M

    K. Anagnostopoulos, M. Axenides, E. Floratos, and N. Tetradis, Physical Review D 64, 125006 (2001)

    2001

  51. [59]

    Loiko, I

    V. Loiko, I. Perapechka, and Y. Shnir, Physical Review D 98, 045018 (2018). 43

    2018

  52. [60]

    Tamaki and N

    T. Tamaki and N. Sakai, Physical Review D 90, 085022 (2014)

    2014

  53. [61]

    A. M. Safian, S. Coleman, and M. Axenides, Nuclear Physics B 297, 498 (1988)

    1988

  54. [62]

    Brihaye and B

    Y. Brihaye and B. Hartmann, Nonlinearity 21, 1937 (2008)

    2008

  55. [63]

    Kusenko, L

    A. Kusenko, L. C. Loveridge, and M. Shaposhnikov, JCAP 08, 011, arXiv:astro-ph/0507225

    arXiv

  56. [65]

    Ansari, L

    A. Ansari, L. Singh Bhandari, and A. M. Thalapillil, Phys. Rev. D 109, 023003 (2024), arXiv:2302.11590 [hep-ph]

    2024 arXiv

  57. [66]

    A. D. Dolgov, S. L. Dubovsky, G. I. Rubtsov, and I. I. Tkachev, Phys. Rev. D 88, 117701 (2013)

    2013

  58. [67]

    S. H. S. Alexander, M. E. Peskin, and M. M. Sheikh-Jabbari, Phys. Rev. Lett. 96, 081301 (2006)

    2006

  59. [68]

    S. N. Gninenko, N. V. Krasnikov, and A. Rubbia, Phys. Rev. D 75, 075014 (2007)

    2007

  60. [69]

    Badertscher, P

    A. Badertscher, P. Crivelli, W. Fetscher, U. Gendotti, S. N. Gninenko, V. Postoev, A. Rubbia, V. Samoylenko, and D. Sillou, Phys. Rev. D 75, 032004 (2007)

    2007

  61. [70]

    Khoury, SciPost Physics Lecture Notes , 042 (2022)

    J. Khoury, SciPost Physics Lecture Notes , 042 (2022)

    2022

  62. [71]

    Berezhiani and J

    L. Berezhiani and J. Khoury, Physical Review D 92, 103510 (2015)

    2015

  63. [72]

    Mistele, S

    T. Mistele, S. McGaugh, and S. Hossenfelder, Astron. Astrophys. 664, A40 (2022), arXiv:2201.07282 [astro-ph.GA]

    2022 arXiv

  64. [73]

    Berezhiani and J

    L. Berezhiani and J. Khoury, Phys. Lett. B 753, 639 (2016), arXiv:1506.07877 [astro-ph.CO]

    2016 arXiv

  65. [74]

    S. R. Coleman, Nucl. Phys. B 262, 263 (1985), [Addendum: Nucl.Phys.B 269, 744 (1986)]

    1985

  66. [75]

    Astrakharchik and L

    G. Astrakharchik and L. Pitaevskii, Physical Review A 70, 013608 (2004)

    2004

  67. [76]

    T. D. Lee and Y. Pang, Phys. Rept. 221, 251 (1992)

    1992

  68. [77]

    Friedberg, T

    R. Friedberg, T. D. Lee, and A. Sirlin, Phys. Rev. D 13, 2739 (1976)

    1976

  69. [78]

    Heeck, A

    J. Heeck, A. Rajaraman, R. Riley, and C. B. Verhaaren, Phys. Rev. D 103, 045008 (2021), arXiv:2009.08462 [hep-th]

    2021 arXiv

  70. [79]

    Heeck and M

    J. Heeck and M. Sokhashvili, Phys. Rev. D 107, 016006 (2023), arXiv:2211.00021 [hep-ph]

    2023 arXiv

  71. [80]

    Paccetti Correia and M

    F. Paccetti Correia and M. G. Schmidt, Eur. Phys. J. C 21, 181 (2001), arXiv:hep- th/0103189

    2001

  72. [81]

    Grojean, G

    C. Grojean, G. Servant, and J. D. Wells, Phys. Rev. D 71, 036001 (2005), arXiv:hep- ph/0407019. 44

    2005

  73. [82]

    Buttazzo, G

    D. Buttazzo, G. Degrassi, P. P. Giardino, G. F. Giudice, F. Sala, A. Salvio, and A. Strumia, Journal of High Energy Physics 2013, 1 (2013)

    2013

  74. [83]

    M. I. Tsumagari, arXiv:0910.3845 (2009)

    2009 arXiv

  75. [84]

    R. H. Brandenberger, Rev. Mod. Phys. 57, 1 (1985)

    1985

  76. [85]

    J. R. Espinosa, G. F. Giudice, E. Morgante, A. Riotto, L. Senatore, A. Strumia, and N. Tetradis, Journal of High Energy Physics 2015, 1 (2015)

    2015

  77. [86]

    Quiros, in ICTP Summer School in High-Energy Physics and Cosmology (1999) pp

    M. Quiros, in ICTP Summer School in High-Energy Physics and Cosmology (1999) pp. 187– 259, arXiv:hep-ph/9901312

    1999 arXiv

  78. [87]

    Boyanovsky, H

    D. Boyanovsky, H. J. de Vega, and R. Holman, in2nd Journee Cosmologique within the frame- work of the International School of Astrophysics, D. Chalonge (1994) arXiv:hep-th/9412052

    1994 arXiv

  79. [88]

    Postma, Physical Review D 65, 085035 (2002)

    M. Postma, Physical Review D 65, 085035 (2002)

    2002

  80. [89]

    Dolgov and J

    A. Dolgov and J. Silk, Physical Review D 47, 3144 (1993)

    1993

  81. [90]

    Kushwaha and S

    A. Kushwaha and S. Shankaranarayanan, Phys. Rev. D102, 103528 (2020), arXiv:2008.10825 [gr-qc]

    2020 arXiv

  82. [91]

    Kushwaha and S

    A. Kushwaha and S. Shankaranarayanan, Phys. Rev. D104, 063502 (2021), arXiv:2103.05339 [hep-ph]

    2021 arXiv

  83. [92]

    Kusenko, Physics Letters B 406, 26 (1997)

    A. Kusenko, Physics Letters B 406, 26 (1997)

    1997

  84. [93]

    Sakai and M

    N. Sakai and M. Sasaki, Progress of theoretical physics 119, 929 (2008)

    2008

  85. [94]

    J.-W. Lee, J. Korean Phys. Soc. 54, 2622 (2009), arXiv:0801.1442 [astro-ph]

    2009 arXiv

  86. [95]

    J. A. Frieman, A. V. Olinto, M. Gleiser, and C. Alcock, Phys. Rev. D 40, 3241 (1989)

    1989

  87. [96]

    Freese, M

    K. Freese, M. Lisanti, and C. Savage, Rev. Mod. Phys. 85, 1561 (2013), arXiv:1209.3339 [astro-ph.CO]

    2013 arXiv

  88. [97]

    Sofue, Publications of the Astronomical Society of Japan 64, 75 (2012)

    Y. Sofue, Publications of the Astronomical Society of Japan 64, 75 (2012)

    2012

  89. [98]

    L. Hui, J. P. Ostriker, S. Tremaine, and E. Witten, Phys. Rev. D 95, 043541 (2017)

    2017

  90. [99]

    M. E. Peskin and D. V. Schroeder, An Introduction to quantum field theory (Addison-Wesley, Reading, USA, 1995)

    1995

  91. [100]

    Mielczarek, T

    J. Mielczarek, T. Stachowiak, and M. Szydlowski, Int. J. of Mod. Phys. D 19, 1843 (2010). 45

    2010

  92. [101]

    L. Hui, A. Joyce, M. J. Landry, and X. Li, Journal of Cosmology and Astroparticle Physics 2021 (01), 011

    2021

  93. [102]

    Kushwaha and S

    A. Kushwaha and S. Shankaranarayanan, Phys. Rev. D101, 065008 (2020), arXiv:1912.01393 [hep-th]

    2020 arXiv

  94. [103]

    Mauland and Ø

    R. Mauland and Ø. Elgarøy, Journal of Cosmology and Astroparticle Physics 2022 (01), 044

    2022

  95. [105]

    M. S. Turner and L. M. Widrow, Phys. Rev. D 37, 2743 (1988). 46

    1988

  96. [370]

    270, 365 (1983)

    Research supported by the US-Israel Binational Science Foundation. 270, 365 (1983)

    1983

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