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Freeze-in Production of Dark Matter Prior to Early Matter Domination

T0 review · 2 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Dark matter produced before an early matter-dominated era can account for the full observed relic abundance, even for weak-scale masses and very small annihilation cross sections.

desk verdict Solid extension of EMD freeze-in to pre-EMD production, but the 'freeze-in' label is stretched: the early-equilibrium plateau is a hot relic, and the headline results assume a constant annihilation cross section. read the letter →

arxiv 1909.01457 v2 pith:BIKOAE3C submitted 2019-09-03 hep-ph astro-ph.COhep-th

Rouzbeh Allahverdi , Jacek K. Osiński This is my paper · ORCID
classification hep-phastro-ph.COhep-th PACS 95.35.+d98.80.Cq
keywords darkmatterfreeze-inearlydominationrelicabundancechemicalequilibriumnon-standardthermalhistoryFIMPBoltzmannequations
topics Dark Matter
open problems Dark Matter
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, in a post-inflationary universe that first passes through a radiation-dominated phase and then through an early matter-dominated (EMD) phase, dark matter produced during that earlier radiation phase can supply most of today's dark matter. This matters for weak-scale masses and for annihilation cross sections too small for ordinary freeze-out, the regime known as freeze-in, where particles are slowly built up from the hot bath. The pre-EMD contribution depends on the full thermal history—the maximum temperature after reheating ($T_{\rm MAX}$), the temperature at the onset of matter domination ($T_O$), and the reheat temperature at its end ($T_R$)—so the allowed parameter space cannot be read off from the EMD era alone. In a broad early-equilibrium regime, dark matter starts in chemical equilibrium while relativistic and decouples later, making the final abundance nearly independent of the annihilation cross section; avoiding overproduction then forces $m_\chi \lesssim 1.6\,g_{*\mathrm{dec}}\,(T_O/10^9\,T_R)\,\mathrm{GeV}$.

What carries the argument

The machinery is the temperature-history map of the non-standard era, fixed by the three temperatures $T_{\rm MAX}$, $T_O$, and $T_R$, with scaling laws $T\propto H^{1/2}$ during radiation domination, $T\propto H^{2/3}$ during the memory phase, and $T\propto H^{1/4}$ during the entropy-producing part of EMD. Inserted into the coupled Boltzmann equations for radiation, the decaying matter component, and the dark-matter number density, these scalings show that the DM production rate falls more slowly than the Hubble rate at early times, so the dominant contribution comes from the highest temperature in each pre-EMD phase. The threshold separating the two regimes is $\langle\sigma_{\rm ann}v\rangle_{\rm f} \sim g_{*\mathrm{MAX}}^{1/2}/(M_P T_{\rm MAX})$; below it dark matter never equilibrates, above it dark matter decouples while relativistic, and the second branch is what makes the abundance cross-section-independent.

What would settle it

Compute the temperature exponent $n$ in $\langle\sigma_{\rm ann}v\rangle_{\rm f}\propto T^n$ for a concrete particle model. For $n < -3/2$, as in the FIMP case with a mediator lighter than the dark-matter particle, the paper's own appendix shows that early production in the radiation and memory phases is suppressed and the expanded parameter regions vanish. Alternatively, an independent measurement of $m_\chi$, $T_O$, and $T_R$ that violates $m_\chi < 1.6\,g_{*\mathrm{dec}}\,(T_O/10^9\,T_R)\,\mathrm{GeV}$ would imply overproduction in the early-equilibrium regime.

Watch

Extended reading notes

Core claim

The central discovery is that production prior to the EMD era—both in the radiation-dominated phase and in the 'memory phase' at the start of EMD, when leftover radiation still dominates over decay products—can dominate the dark-matter relic abundance. Working with a thermally averaged annihilation cross section $\langle\sigma_{\rm ann}v\rangle_{\rm f}$ that is constant between $T_R$ and $T_{\rm MAX}$, the authors show that the pre-EMD contribution is the largest at the highest temperature in each phase. When $\langle\sigma_{\rm ann}v\rangle_{\rm f}$ is so small that dark matter never reaches equilibrium, the relic abundance is set at $T_{\rm MAX}$; when it is larger, dark matter begins in chemical equilibrium and decouples while relativistic, leaving a comoving number density determined by the decoupling temperature and by $T_O$. In that early-equilibrium regime the relic abundance is essentially independent of the cross section, and not overproducing dark matter gives the inequality $m_\chi \lesssim 1.6\,g_{*\mathrm{dec}}\,(T_O/10^9\,T_R)\,\mathrm{GeV}$.

Load-bearing premise

The load-bearing premise is that the dark-matter annihilation cross section stays constant over the whole temperature interval from $T_R$ to $T_{\rm MAX}$; if it falls steeply as the universe cools, the early pre-matter-era production that the paper relies on is suppressed and the newly opened parameter space disappears.

Editorial extensions

If this is right

  • The allowed $m_\chi$–$\langle\sigma_{\rm ann}v\rangle_{\rm f}$ plane gains large regions at very small cross sections, down to values that the EMD-only freeze-in analysis would exclude.
  • In the early-equilibrium regime, the dark-matter relic abundance is set almost entirely by $m_\chi$ and the ratio $T_O/T_R$, so measuring $m_\chi$ at a collider plus cosmological bounds on that ratio can test the scenario even if direct and indirect detection see nothing.
  • The pre-EMD contribution scales linearly with $m_\chi$ and only mildly with $T_R$, in contrast to the steep $m_\chi^{-5}$ of late-EMD freeze-in, so changing the thermal history reshuffles which masses are viable.
  • If the cross section grows with temperature ($n>0$), pre-EMD production can dominate even for very small cross sections at the mass scale, while for $n<-3/2$ (for example the FIMP with $n=-2$) the newly opened parameter space disappears.

Reading between the lines

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

  • The same 'look before the non-standard epoch' logic should apply to other early phases with a high-temperature radiation stage, such as kination or a burst of fast expansion; computing freeze-in there would show whether the $T_O/T_R$ bound generalizes.
  • In the early-equilibrium regime dark-matter particles decouple while relativistic, so their momentum distribution may carry memory of the pre-EMD epoch; the paper does not examine consequences for structure formation or direct-detection kinematics.
  • The inequality $m_\chi < 1.6\,g_{*\mathrm{dec}}\,(T_O/10^9\,T_R)\,\mathrm{GeV}$ can be read in reverse as a falsifiable prediction: once gravitational-wave or CMB experiments pin down $T_O/T_R$, a stable weak-scale particle found above the bound would rule the early-equilibrium branch out.
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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

2 major / 5 minor

Summary. This paper studies dark matter production in a post-inflationary thermal history with a radiation-dominated (RD) epoch followed by an early matter-dominated (EMD) epoch. Assuming a constant velocity-averaged annihilation cross section <σannv>f over T_R ≲ T ≲ T_MAX, the authors derive analytic expressions for the DM relic abundance generated before the entropy-producing phase of EMD. Two regimes are identified: a decoupling regime in which production is dominated by the highest temperature T_MAX (first line of Eq. (7)) and an early-equilibrium regime in which DM starts in chemical equilibrium and decouples while relativistic, so the abundance is essentially independent of <σannv>f (second line of Eq. (7)). This leads to the upper bound m_χ ≲ 1.6 g_*dec (T_O/(10^9 T_R)) (1 GeV) in Eq. (9). Numerical solutions of the coupled Boltzmann equations (Eq. (8)) confirm the analytic formulas and map the allowed regions of the m_χ-<σannv>f plane for several thermal histories.

Significance. The analytic machinery is careful and the paper provides useful closed-form expressions for the pre-EMD contribution, including the memory phase, and these derivations are parameter-free in the sense that the observed relic abundance is used as a constraint rather than a fitted input. The early-equilibrium bound Eq. (9) is a clean relation between the DM mass and the duration of EMD, and the discussion of gravitational-wave and microhalo observables is a valuable addition. However, the paper's general claim that freeze-in prior to EMD dominates is not valid for the canonical FIMP realization, as the Appendix shows for n < -3/2; it applies only to constant or non-negative power-law cross sections. In addition, the early-equilibrium regime is physically a hot relativistic relic rather than freeze-in. These two issues affect the framing of the central results and require revision, but the underlying calculations should remain valid once the scope is stated accurately.

major comments (2)
  1. [Section V and Appendix B, Eqs. (20) and (7)] The central claim that pre-EMD production dominates in the freeze-in regime is derived under the assumption of a constant <σannv>f. The final paragraph of the Appendix shows that if <σannv>f ∝ T^n, the integrals in Eq. (20) are dominated by their upper limits only for n ≥ -1 in the RD phase and n ≥ -3/2 in the memory phase; for n < -3/2, in particular the canonical FIMP case n = -2, production is instead peaked near T ~ m_χ and the pre-EMD contribution no longer dominates. The paper does acknowledge this at the end of Section V, but the abstract, the introduction, Eq. (7), Eq. (9), and the description of regions 2 and 3 in Section III present the result as a general freeze-in statement. These statements should be explicitly restricted to constant <σannv>f (or n ≥ -1), and the FIMP case with n = -2 should be presented as a counterexample to the general claim.
  2. [Section II.B and Section IV] The 'early-equilibrium regime' is not freeze-in. In this regime DM particles begin in chemical equilibrium and decouple while relativistic, and the relic abundance is fixed by the equilibrium comoving density at decoupling (Eqs. (23) and (24)), exactly as in the standard hot-relativistic-relic case such as neutrino decoupling. Calling this a 'freeze-in analogue' and including it under the freeze-in label conflates two distinct production mechanisms. This matters because the plateau in region 2 of Fig. 2 and the inequality in Eq. (9) are hot-relic results, not freeze-in results. The terminology should be changed to 'early chemical decoupling' or 'hot relativistic relic,' and the abstract's statement that the paper focuses on freeze-in should be adjusted accordingly.
minor comments (5)
  1. [Section I] In the first paragraph, 'significant affect' should be 'significant effect.'
  2. [Abstract and Section II.B] The statement that DM particles decouple 'during early matter domination' is imprecise; the body of the paper places decoupling at H_tran ≲ H ≲ H_MAX, which spans the prior RD phase and the memory phase of EMD. Please rephrase to 'prior to the entropy-producing phase of EMD.'
  3. [Section III, Fig. 2 caption] Region 0 is defined only in the caption; the bulleted list in the text should also explain it explicitly alongside regions 1-3.
  4. [Section IV] The phrase 'freeze-in analogue to the WIMP miracle' should be removed in favor of a hot-relic description, given the reclassification suggested in the major comment.
  5. [Section II.B, Eq. (7)] The factors (10^9 T_MAX T_R / T_O) and (10^9 T_R / T_O) would benefit from an explicit statement that T_MAX, T_O, and T_R are in GeV.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central relic-abundance formulas are derived from the stated Boltzmann equations under an explicit constant-cross-section assumption, and the only self-citations are auxiliary, non-load-bearing.

full rationale

This paper contains no circular derivation. The pre-EMD relic abundances in Eqs. (7), (21), and (24) are obtained by integrating the Boltzmann equations (19)-(20) under the explicitly stated assumption that the thermally averaged annihilation cross section is constant over the temperature range of interest, T_R < T < T_MAX (Section II and Appendix B). The early-equilibrium formula (24) follows from comoving entropy conservation after chemical decoupling, while the decoupling formula (21) follows from evaluating the integrals in (20) at their upper limits. Eq. (9) is then obtained by equating the early-equilibrium abundance to the observed Omega h^2 = 0.12, which is used as a constraint rather than as a fitted input. The cited temperature-evolution relations from the authors' own previous work [26] are not load-bearing: Eqs. (4)-(5) are derived in the text from the standard T-H relation (3) with the appropriate redshift behavior, and the self-citation is only an auxiliary cross-check. The Appendix's final paragraph explicitly limits the main results to n >= -1 and excludes the canonical FIMP case with n = -2, so the constant-cross-section assumption is a stated scope condition, not a concealed input. The early-equilibrium regime reproduces a known relativistic hot-decoupling abundance, but this is a labeling and scope issue rather than a derivation that reduces to its own input. No prediction in the paper is equivalent by construction to a fitted parameter or to a self-citation, and no uniqueness theorem is imported from the authors' prior work. The paper is therefore self-contained for the class of models it analyzes.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central calculation depends on the three cosmological temperatures and the dark matter mass/cross section as input parameters, plus standard cosmology and the stated assumptions of prompt thermalization, single dark matter degree of freedom, constant cross section, and no reheating production. No new particles or forces are introduced.

free parameters (5)
  • TMAX
    Maximum temperature of the radiation-dominated phase after inflationary reheating; scanned in Figs. 3 and 4. Sets the threshold for early-equilibrium and the scale of decoupling-regime production.
  • TO
    Temperature at onset of early matter domination; scanned from 10^8 to 10^10 GeV. Controls dilution and the position of the early-equilibrium plateau.
  • TR
    Reheating temperature at end of early matter domination; scanned in Figs. 3 and 5. Together with TO sets the duration of EMD and the entropy dilution.
  • m_chi
    Dark matter mass, scanned across the relic-abundance curves; central variable of the parameter-space maps.
  • <sigma_ann v>_f
    Velocity-averaged annihilation cross section at the relevant temperature, scanned over many decades; central variable. Assumed constant over T_R to T_MAX in the main calculation.
assumptions (6)
  • standard math Friedmann equations and standard FRW cosmology govern the expansion of the universe.
    Used as the background for all Boltzmann equations in Eq. (8) and the temperature-redshift relations.
  • domain assumption Decay products of the field driving early matter domination thermalize promptly, forming an instantaneous radiation bath.
    Used for Eq. (1) and the temperature history; slow thermalization would change the freeze-in yield. The paper relies on footnote 3.
  • domain assumption Dark matter is a single species with one degree of freedom, produced only from thermal bath annihilations, with no significant direct production from phi decay.
    Assumed in Section II and used in the Boltzmann equations; direct decay adds another source and tightens the overproduction bound.
  • domain assumption The thermally averaged annihilation cross section is constant over T_R < T < T_MAX, as for dimension-5 operators with mediator mass above T_MAX.
    Stated in Section II; later relaxed in Section V and Appendix B, where strong temperature dependence (n < -3/2) suppresses early production.
  • domain assumption Temperature evolution during the pre-EMD radiation and memory phases follows Eqs. (3) and (5), taken from the same authors' earlier work [26].
    The memory-phase relation is imported from prior literature; different initial radiation abundances would alter the dilution and pre-EMD yields.
  • domain assumption No significant dark matter production occurs during inflationary reheating itself.
    Footnote 1 states this model-dependent contribution is ignored; it would only strengthen pre-EMD production.

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Pith. "Pith review of Freeze-in Production of Dark Matter Prior to Early Matter Domination." pith.science (2026). https://pith.science/paper/BIKOAE3C

@misc{pith2026190901457,
  author       = {Pith},
  title        = {Pith review of: Freeze-in Production of Dark Matter Prior to Early Matter Domination},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BIKOAE3C}},
  note         = {Machine review of arXiv:1909.01457}
}
abstract

Freeze-out or freeze-in during a period of early matter domination can yield the correct dark matter abundance for small values of the velocity-averaged annihilation cross section, $\langle \sigma_{\rm ann} v \rangle_{\rm f} < 3 \times 10^{-26}$ cm$^3$ s$^{-1}$. However, in a generic non-standard thermal history, such a period is typically preceded by other phases. Here, we study production of dark matter in a simple post-inflationary history where a radiation-dominated phase after reheating is followed by an epoch of early matter domination. Focusing on the freeze-in regime, we show that dark matter production prior to early matter domination can dominate the relic abundance in large parts of the parameter space, including weak scale dark matter masses, and the allowed regions are highly dependent on the entire post-inflationary history. Moreover, for a very broad range of $\langle \sigma_{\rm ann} v \rangle_{\rm f}$ spanning over several decades, dark matter particles can start in chemical equilibrium early on and decouple during early matter domination, thereby rendering the relic abundance essentially independent of $\langle \sigma_{\rm ann} v \rangle_{\rm f}$. We briefly discuss connections to different observables as a possible means to test the elusive freeze-in scenario in this case.

Figures

Figures reproduced from arXiv: 1909.01457 by the authors.

Figure 1
Figure 1. FIG. 1: Temperature of the universe as a function of the Hubble expansion rate showing the post-inflationary [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Values of [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Variation of the curve from Fig. 2 for different values of [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Variation of the curve from Fig. 2 for different values of [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: Left: variation of [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Contours of the upper bound on [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Upper bound on the DM mass [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

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Reference graph

Works this paper leans on

59 extracted references · 14 canonical work pages · cited by 1 Pith paper

  1. [1]

    Bertone, D

    G. Bertone, D. Hooper, and J. Silk, Phys. Rept. 405, 279 (2005) [e-Print: hep-ph/0404175]

    arXiv 2005

  2. [2]

    Ackermann et al

    M. Ackermann et al. [Fermi-LAT Collaboration], Phys. Rev. Lett. 115, 231301 (2015) [e-Print: arXiv:1503.02641 [astro- ph.HE]]

    arXiv 2015

  3. [3]

    Albert et al

    A. Albert et al. FERMI-LAT and DES Collaborations], Astrophys. J. 834, 110 (2017) [e-Print: arXiv:1611.03184 [astro- ph.HE]]

    arXiv 2017

  4. [4]

    R. K. Leane, T. R. Slatyer, J. F. Beacom, and K. C. Y. Ng, Phys. Rev. D 98, 023016 (2018) e-Print: arXiv:1805.10305 [hep-ph]

    arXiv 2018

  5. [5]

    Kamionkowski and M

    M. Kamionkowski and M. S. Turner, Phys. Rev. D 42, 3310 (1990)

    work page 1990

  6. [6]

    G. Kane, K. Sinha, and S. Watson, Int. J. Mod. Phys. D 24, 1530022 (2015)

    work page 2015

  7. [7]

    G. F. Giudice, E. W. Kolb, and A. Riotto, Phys. Rev. D 64, 023508 (2001)

    work page 2001

  8. [8]

    A. L. Erickcek, Phys. Rev. D 92, 103505 (2015) [e-Print: arXiv:1504.03335 [astro-ph.CO]]

    arXiv 2015

Show all 59 references
  1. [9]

    Berlin, D

    A. Berlin, D. Hooper and G. Krnjaic, Phys. Lett. B 760, 106 (2016) [e-Print: arXiv:1602.08490 [hep-ph]]

    2016 arXiv

  2. [10]

    D’Eramo, N

    F. D’Eramo, N. Fernandez and St. Profumo, JCAP 1705, 012 (2017) [e-Print: arXiv:1703.04793 [hep-ph]]

    2017 arXiv

  3. [11]

    Redmond and A

    K. Redmond and A. L. Erickcek, Phys. Rev. D 96, 043511 (2017) [e-Print: arXiv:1704.01056 [hep-ph]]

    2017 arXiv

  4. [12]

    Visinelli, Symmetry 10, 546 (2018) [e-Print: arXiv:1710.11006 [astro-ph.CO]]

    L. Visinelli, Symmetry 10, 546 (2018) [e-Print: arXiv:1710.11006 [astro-ph.CO]]

    2018 arXiv

  5. [13]

    Maldonado and J

    C. Maldonado and J. Unwin, JCAP 1906, 037 (2019) [e-Print: arXiv:1902.10746 [hep-ph]]

    2019

  6. [14]

    Allahverdi, R

    R. Allahverdi, R. Brandenberger, F-Y Cyr-Racine, and A. Mazumdar, Ann. Rev. Nucl. Part. Sci. 60, 27 (2010) [e-Print: arXiv:1001.2600 [hep-th]]

    2010 arXiv

  7. [15]

    M. A. Amin, M. P. Hertzberg, D. I. Kaiser, and J. Karouby, Int. J. Mod. Phys. D 24, 1530003 (2014) [e-Print: arXiv:1410.3808 [hep-ph]]

    2014 arXiv

  8. [16]

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

    2016 arXiv

  9. [17]

    Berlin, D

    A. Berlin, D. Hooper, and G. Krnjaic, Phys. Rev. D 94, 095019 (2016) [e-Print: arXiv:1609.02555 [hep-ph]]

    2016 arXiv

  10. [18]

    J. A. Dror, E. Kuflik, B. Melcher, and S. Watson, Phys. Rev. D 97, 063524 (2018) [e-Print: arXiv:1711.04773 [hep-ph]]

    2018 arXiv

  11. [19]

    Cirelli, Y

    M. Cirelli, Y. Gouttenoire, K. Petraki, and F. Sala, JCAP 1902, 014 (2019) [e-Print: arXiv:1811.03608 [hep-ph]]

    2019 arXiv

  12. [20]

    Bernal, M

    N. Bernal, M. Heikinheimo, T. Tenkanen, K. Tuominen, and V. Vaskonen, Int. J. Mod. Phys. A 32, 1730023 (2017) [e-Print: arXiv:1706.07442 [hep-ph]]

    2017 arXiv

  13. [21]

    Allahverdi and M

    R. Allahverdi and M. Drees, Phys. Rev. D 66, 063513 (2002) [e-Print: hep-ph/0205246]

    2002 arXiv

  14. [22]

    Harigaya, M

    K. Harigaya, M. Kawasaki, K. Mukaida and M. Yamada, Phys. Rev. D 89, 083532 (2014) [e-Print: arXiv:1402.2846 [hep-ph]]

    2014 arXiv

  15. [23]

    M. A. G. Garcia and M. A. Amin, Phys. Rev. D 98, 103504 (2018) [e-Print: arXiv:1806.01865 [hep-ph]]

    2018 arXiv

  16. [24]

    Harigaya, K

    K. Harigaya, K. Mukaida and M. Yamada, JHEP 1907, 059 (2019) [e-Print: arXiv:1901.11027 [hep-ph]]. 15

    2019 arXiv

  17. [25]

    Harigaya and K

    K. Harigaya and K. Mukaida, JHEP 1405, 006 (2014) [e-Print: arXiv:1312.3097 [hep-ph]]

    2014 arXiv

  18. [26]

    Allahverdi and J

    R. Allahverdi and J. K. Osinski, Phys. Rev. D 99, 083517 (2019) [e-Print: arXiv:1812.10522 [hep-ph]]

    2019 arXiv

  19. [27]

    Drees and F

    M. Drees and F. Hajkarim, JCAP 1802, 057 (2018) [e-Print: arXiv:1711.05007]

    2018 arXiv

  20. [28]

    Kawasaki, T

    M. Kawasaki, T. Moroi, and T. Yanagida, Phys. Lett. B 370, 52 (1996) [e-Print: hep-ph/9509399]

    1996 arXiv

  21. [29]

    Moroi and L

    T. Moroi and L. Randall, Nucl. Phys. B 570, 455 (2000) [e-Print: hep-ph/9906527]

    2000 arXiv

  22. [30]

    G. B. Gelmini and P. Gondolo, Phys. Rev. D 74, 023510 (2006) [e-Print: hep-ph/0602230]

    2006 arXiv

  23. [31]

    Allahverdi, B

    R. Allahverdi, B. Dutta, and K. Sinha, Phys. Rev. D 83, 083502 (2011) [e-Print: arXiv:1011.1286 [hep-ph]]

    2011 arXiv

  24. [32]

    A. R. Liddle and S. M. Leach, Phys. Rev. D 68, 103503 (2003) [e-Print: astro-ph/0305263]

    2003 arXiv

  25. [33]

    Rehagen and G

    T. Rehagen and G. B. Gelmini, JCAP 1506, 039 (2015) [e-Print: arXiv:1504.03768 [hep-ph]]

    2015 arXiv

  26. [34]

    D. I. Podolsky, G. N. Felder, L. Kofman, and M. Peloso, Phys. Rev. D 73, 023501 (2006) [e-Print: hep-ph/0507096]

    2006 arXiv

  27. [35]

    K. D. Lozanov and M. A. Amin, Phys. Rev. Lett. 119, 061301 (2017) [e-Print: arXiv:1608.01213 [astro-ph.CO]]

    2017 arXiv

  28. [36]

    Akrami et al [PLANCK Collaboration], arXiv:1807.06211 [astro-ph.CO]

    Y. Akrami et al [PLANCK Collaboration], arXiv:1807.06211 [astro-ph.CO]

    arXiv

  29. [37]

    Roest, JCAP 1401, 007 (2014) [e-Print: arXiv:1309.1285 [hep-th]]

    D. Roest, JCAP 1401, 007 (2014) [e-Print: arXiv:1309.1285 [hep-th]]

    2014 arXiv

  30. [38]

    Allahverdi, K

    R. Allahverdi, K. Dutta, and A. Maharana, JCAP 1810, 038 (2018) [e-Print: arXiv:1808.02659 [astro-ph.CO]]

    2018 arXiv

  31. [39]

    Durrer and J

    R. Durrer and J. Hasenkamp, Phys. Rev. D 84, 064027 (2011) [e-Print: arXiv:1105.5283 [gr-qc]]

    2011 arXiv

  32. [40]

    Jinno, T

    R. Jinno, T. Moroi, and K. Nakayama, JCAP 1401, 040 (2014) [e-Print: arXiv:1307.3010 [hep-ph]]

    2014 arXiv

  33. [41]

    D’Eramo and K

    F. D’Eramo and K. Schmitz, Phys. Rev. Research 1, 013010 (2019) e-Print: arXiv:1904.07870 [hep-ph]

    2019 arXiv

  34. [42]

    Bernal and F

    N. Bernal and F. Hajkarim, e-Print: arXiv:1905.10410 [astro-ph.CO]

    1905 arXiv

  35. [43]

    D. G. Figueroa and E. H. Tanin, JCAP 1908, 011 (2019) e-Print: arXiv:1905.11960 [astro-ph.CO]

    2019 arXiv

  36. [44]

    Blanco, M

    Ca. Blanco, M. Sten Delos, A. L. Erickcek and D. Hooper, e-Print: arXiv:1906.00010 [astro-ph.CO]

    1906 arXiv

  37. [45]

    Sten Delos, T

    M. Sten Delos, T. Linden and A. L. Erickcek, e-Print: arXiv:1910.08553 [astro-ph.CO]

    1910 arXiv

  38. [46]

    M. Dine, W. Fischler, and D. Nemeschansky, Phys. Lett. B 136, 169 (1984)

    1984

  39. [47]

    G. D. Coughlan, R. Holman, P. Ramond, and G. G. Ross, Phys. Lett. B 140, 44 (1984)

    1984

  40. [48]

    A. S. Goncharov, A. D. Linde, and M. I. Vysotsky, Phys. Lett. B 147, 279 (1984)

    1984

  41. [49]

    M. Dine, L. Randall, and S. D. Thomas, Nucl. Phys. B 458, 291 (1996) [e-Print: hep-ph/9507453]

    1996 arXiv

  42. [50]

    Cicoli, K

    M. Cicoli, K. Dutta, A. Maharana, and F. Quevedo, JCAP 1608, 006 (2016) [e-Print: arXiv:1604.08512[hep-th]]

    2016 arXiv

  43. [51]

    Allahverdi, B

    R. Allahverdi, B. Dutta, and K. Sinha, Phys. Rev. D 86, 095016 (2012) [e-Print: arXiv:1208.0115 [hep-ph]]

    2012 arXiv

  44. [52]

    Allahverdi, M

    R. Allahverdi, M. Cicoli, B. Dutta, and K. Sinha, Phys. Rev. D 88, 095015 (2013) [e-Print: arXiv:1307.5086 [hep-ph]]

    2013 arXiv

  45. [53]

    Allahverdi, M

    R. Allahverdi, M. Cicoli, and F. Muia, JHEP 1606, 153 (2016) [e-Print: arXiv:1604.03120 [hep-th]]

    2016 arXiv

  46. [54]

    M. A. G. Garcia, Y. Mambrini, K. A. Olive, and M. Peloso, Phys. Rev. D 96, 103510 (2017) [e-Print: arXiv:1709.01549 [hep-ph]]

    2017 arXiv

  47. [55]

    L. J. Hall, K. Jedamzik, J. March-Russell and S. M. West, JHEP 1003, 080 (2010) [e-Print: arXiv:0911.1120 [hep-ph]]

    2010 arXiv

  48. [56]

    K. S. Babu, R. N. Mohapatra and S. Nasri, Phys. Rev. Lett. 98, 161301 (2007) [e-Print: hep-ph/0612357]

    2007 arXiv

  49. [57]

    Allahverdi, B

    R. Allahverdi, B. Dutta, R. N. Mohapatra and K. Sinha, Phys. Rev. Lett. 111, 051302 (2013) [e-Print: arXiv:1305.0287 [hep-ph]]

    2013 arXiv

  50. [58]

    Allahverdi and B

    R. Allahverdi and B. Dutta, Phys. Rev. D 88, 023525 (2013) [e-Print: arXiv:1304.0711 [hep-ph]]

    2013 arXiv

  51. [59]

    X. Lu, H. Murayama, J. T. Ruderman and K. Tobioka, Phys. Rev. Lett. —bf 112, 191803 (2014) [e-Print: arXiv:1308.0792 [hep-ph]]

    2014 arXiv

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