Constraining Nonthermal Dark Matter's Impact on the Matter Power Spectrum

Adrienne Erickcek; Carisa Miller; Riccardo Murgia

REVIEW 3 major objections 5 minor 75 references

Constraining Nonthermal Dark Matter's Impact on the Matter Power Spectrum

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Dark matter produced during an early matter-dominated era is still relativistic at reheating, so free streaming erases the era's boost to small-scale structure, and observed structures bound the birth velocity ($\gamma_D \lesssim 550$ at…

desk verdict The paper convincingly shows that nonthermal dark matter produced during an EMDE remains relativistic at reheating, wiping out the EMDE perturbation enhancement; the Lyman-alpha-derived exclusion limits are real but less certain than they look because of the transfer-function shape extrapolation. read the letter →

arxiv 1908.10369 v2 pith:LWJAD7UQ submitted 2019-08-27 astro-ph.CO

Carisa Miller , Adrienne Erickcek , Riccardo Murgia This is my paper · ORCID

classification astro-ph.CO

keywords earlymatter-dominatederanonthermaldarkmatterfreestreamingpowerspectrumLyman-alphaforestMilkyWaysatellitesreheatingtemperaturewarm

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

This paper considers dark matter produced nonthermally from the decay of a scalar field that dominates the universe during an early matter-dominated era (EMDE), so that all dark-matter particles start with a single relativistic velocity. The paper claims that despite adiabatic cooling, most of this dark matter is still relativistic at reheating, because new hot particles are created up to the end of the EMDE. The resulting free streaming erases the linear growth of small-scale perturbations that the EMDE would otherwise imprint. The paper then uses observations of the Lyman-$\alpha$ forest and of Milky Way satellite galaxies to set upper limits on the birth velocity as a function of reheat temperature, e.g. $\gamma_D \lesssim 550$ for $T_{RH}=10$ MeV. This matters because it constrains the allowed mass hierarchy and decay properties of any model that produces dark matter this way.

What carries the argument

The load-bearing object is the birth-time distribution $f(a_D)$ of dark-matter particles, obtained from the comoving production rate $d\hat{n}_\chi/da_D \propto \rho_\phi \sqrt{a_D}/H_D$ during the EMDE. This distribution determines the average velocity $\langle v^2\rangle(a)$, the fraction of particles born early enough to be cold at reheating, and—after scaling by the combination $\mu = \gamma_D v_D a_{RH}/a_0$—the present-day momentum distribution that enters the transfer function. The transfer function itself is fitted with the ansatz $T(k) = [1 + (\alpha k)^\beta]^\gamma$, with $\beta$ and $\gamma$ given as analytic functions of $\alpha$, so the whole cosmological constraint reduces to a single cutoff scale $\alpha$. A separate piece of machinery is the analytic free-streaming integral, expressed in terms of $\mu$, which connects $\alpha$ to the physical free-streaming length by a simple power law.

What would settle it

Detect structure on scales the EMDE is supposed to enhance—for instance a population of microhalos corresponding to comoving scales $\lambda \lesssim 30$ pc, or a matter power spectrum at $k \gtrsim 10\,h/\mathrm{Mpc}$ that shows no suppression below the cold-dark-matter prediction—and the central claim that free streaming erases those perturbations is contradicted.

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Extended reading notes

Core claim

The central discovery is that adiabatic cooling cannot rescue nonthermal dark matter in an EMDE. The average dark-matter velocity at reheating stays close to the velocity imparted at decay—for $v_D=0.99$, the rms velocity is still about 0.93—because the continuous creation of fresh relativistic particles offsets the redshift of older ones. Consequently, only a tiny fraction of the dark matter (about 0.15% for $v_D=0.5$) is slow enough at reheating to preserve the factor-of-ten perturbation enhancement that modes entering the horizon at $0.1 a_{RH}$ would otherwise enjoy, and mixed-dark-matter studies imply even that fraction is far too small to matter. On observed scales, the same free streaming suppresses power in the Lyman-$\alpha$ forest and reduces the predicted number of Milky Way satellites. The resulting constraints are phrased in terms of the parameter combination $\mu = \gamma_D v_D a_{RH}/a_0$, which sets both the free-streaming length and the momentum distribution; for a reheat temperature of 10 MeV they require $\gamma_D \lesssim 550$.

Load-bearing premise

The load-bearing assumption is that the model's transfer function is faithfully represented by the fitting form $T(k) = [1 + (\alpha k)^\beta]^\gamma$ with $\beta$ and $\gamma$ fixed as functions of $\alpha$, and that the Lyman-$\alpha$ likelihood computed from precomputed hydrodynamic simulations remains valid when extrapolated to this shape; if the true shape differs where $T(k)$ is small, the quoted $\alpha$ and $\gamma_D$ limits would shift.

Editorial extensions

If this is right

The EMDE enhancement to small-scale structure is preserved only for dark matter born with very low velocity; for a particle born at half the speed of light only about 0.15% of the population is slow enough at reheating ($v_{RH} < 0.01$), so the enhancement is effectively erased.
Lyman-alpha forest data bound the transfer-function cutoff to $\alpha < 0.011\,\mathrm{Mpc}/h$ (68% C.L.) and $\alpha < 0.026\,\mathrm{Mpc}/h$ (95% C.L.), which for a given reheat temperature translates into an upper limit on $\gamma_D$; for $T_{RH}=10$ MeV, $\gamma_D \lesssim 550$.
Milky Way satellite counts give essentially the same 95% cutoff, $\alpha < 0.026\,\mathrm{Mpc}/h$ (equivalently a half-mode scale $k_{hm} > 36\,h/\mathrm{Mpc}$), so the two independent small-scale probes agree.
In the absence of annihilations, matching the observed relic abundance requires the branching fraction $f$ of the decaying scalar into dark matter to be below about $10^{-4}$ in the allowed region, meaning annihilations or another depletion mechanism are needed to avoid fine-tuning.
The constraints can be recast as limits on the scalar decay rate $\Gamma_\phi$ and on the parent-daughter mass hierarchy ($m_\phi = 2\gamma_D m_\chi$), connecting the cosmological bound to particle-physics parameters.

Reading between the lines

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

Because the cutoff depends on the single combination $\mu = \gamma_D v_D a_{RH}/a_0$, any nonthermal production mechanism with the same birth-time distribution and the same $\mu$ should show the same cutoff scale, so the bounds are transferable beyond the specific two-body decay considered.
If future Lyman-alpha measurements or satellite catalogs push the cutoff below $\alpha \approx 0.011\,\mathrm{Mpc}/h$, the allowed region would contract toward lower $\gamma_D$; if they relax it, higher birth velocities would open up.
A broader, non-monoenergetic distribution of birth velocities could change the shape of the transfer function and shift the limits, depending on the high-velocity tail; this is a natural next step left by the paper.
If dark matter can exchange momentum with Standard Model particles after production, the velocity distribution would cool more efficiently, potentially reviving the EMDE microhalo signature; searches for microhalos at pc scales would then discriminate between this minimal model and models with interactions.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

The thing to know: this paper settles a question that's been hovering over EMDE dark matter. Ref. [51] assumed all dark matter was born at reheating; Miller et al. derive the actual birth-time distribution across the whole EMDE and show that for relativistic production the bulk of dark matter is still relativistic at reheating, so the much-touted EMDE perturbation enhancement is erased. That result is new, cleanly derived, and I think it's right.

What's good: Sections II and III are a model of honest analytic cosmology. The integrals for average velocity and birth-time distribution are self-contained, the approximations are stated, and the qualitative conclusion is robust to the details—you'd need vD <~ 0.02 at birth to get even a percent of dark matter below v = 0.01 at reheating. The Milky Way satellite constraint (khm > 36 h/Mpc, leading to alpha < 0.026) is on solid ground because it depends mainly on the half-mode scale, not the detailed high-k shape.

The soft spot is the Lyman-alpha bound. The authors feed their transfer function fit into the precomputed MCMC likelihood of Ref. [67], using beta and gamma as analytic functions of alpha. But their gamma is about -1.1, while the thermal WDM templates in the simulation grid have gamma = -4.46. That's a factor-of-three difference in the high-k slope, and the text admits the likelihood is linearly extrapolated when parameters fall outside the template. The Lyman-alpha flux power spectrum is shape-sensitive, so the quoted gamma_D <~ 550 at TRH = 10 MeV carries real uncertainty. This doesn't threaten the central qualitative claim, but it means the precise excluded region in Fig. 12 should be treated as provisional until either the transfer function mapping is validated against dedicated simulations or the code is released. No code is shipped, so independent replication takes real work.

Bottom line: a substantive paper, worth a serious referee, and likely to be cited in the EMDE literature despite the Lyman-alpha caveat. I'd send it out; the referees should push for validation of the extrapolation or a clear statement that the Lyman-alpha bounds are indicative.

Referee Report

3 major / 5 minor

Summary. The paper studies nonthermal dark matter production during an early matter-dominated era (EMDE) preceding reheating. The authors model a decaying scalar field that produces both Standard Model radiation and dark matter particles with a common initial velocity v_D, and they derive the resulting dark matter velocity distribution and its evolution. Their central finding is that adiabatic cooling during the EMDE is inefficient: most dark matter particles are still relativistic at reheating, so their free streaming erases the perturbation growth that would otherwise occur during the EMDE. They also compute the matter power spectrum suppression using CLASS and fit the resulting transfer function to the form T(k)=[1+(alpha k)^beta]^gamma, with beta and gamma fixed as functions of alpha. Using a Lyman-alpha forest likelihood from Ref. [67], they derive bounds on alpha, translate them into constraints on the production Lorentz factor gamma_D as a function of reheat temperature T_RH, and find a comparable bound from Milky Way satellite abundances. The headline result is that for T_RH=10 MeV, dark matter must be produced with gamma_D lesssim 550.

Significance. If the quantitative bounds hold, the paper closes an important loophole in the EMDE-enhanced structure formation scenario: it shows that the most natural, non-fine-tuned production of dark matter during an EMDE yields relativistic particles whose free streaming destroys the linear-growth enhancement. The analytic derivation of the birth-time distribution and average velocity in Sections II and III is clean, self-contained, and robust, and it requires no external data. The Milky Way satellite bound is independent of the Lyman-alpha likelihood and depends mainly on the half-mode scale, making it a relatively robust quantitative result. The main weakness is that the headline Lyman-alpha exclusion relies on extrapolating a WDM-calibrated likelihood to a transfer-function shape very different from thermal WDM, so the precise excluded region in Fig. 12 is less certain than the central qualitative claim.

major comments (3)

[Section IV.B, Eq. (34) and Fig. 11] The quantitative Lyman-alpha bounds on alpha, and hence the headline constraint gamma_D lesssim 550 for T_RH = 10 MeV, depend on evaluating the Ref. [67] likelihood for transfer-function shape parameters that are far outside the WDM-like simulation grid. The paper itself states that parameter values outside the template are linearly extrapolated, and the fitted gamma values are approximately -1.1 to -1.35, whereas thermal WDM has gamma = -4.46. This is roughly a factor of three difference in the high-k slope of T(k), and Lyman-alpha flux power is sensitive to the shape of the suppression, not just the half-mode scale. The derived alpha bounds and the corresponding exclusion region in Fig. 12 therefore inherit an unvalidated extrapolation. The authors should either validate the likelihood for this shape with dedicated hydrodynamic simulations, or explicitly present the Lyman-alpha bounds as approximate and make the MW satellite bound the primary quantitative result.
[Section IV.B, Figs. 9-10] The claim that the nonthermal transfer function is 'quite similar' to thermal WDM is based on matching the half-mode scale, but the two shapes differ substantially at T(k) lesssim 0.1 because of the different gamma. Since the Lyman-alpha likelihood is mapped through the full fitting form, the alpha approximately 2 alpha_WDM relation cannot by itself justify using the WDM-calibrated simulation grid. The MW satellite constraint in Section IV.C, which uses only khm through Eq. (38), is less sensitive to this shape difference and should be presented as the more robust channel; the paper's current emphasis on the Lyman-alpha bound gives a false impression of equal robustness for the two constraints.
[Section IV.B, paragraph on 'Whenever some of the parameters assume values not enclosed by the template'] The manuscript reports the Lyman-alpha bound as a firm result, but the reliance on linear extrapolation is disclosed only in a single sentence. No code or simulation products are released, so the likelihood evaluation for the extrapolated region cannot be independently checked. This is not a critique of the analytic derivation, but it is a load-bearing issue for the quantitative exclusion region: a reader cannot distinguish which part of Fig. 12 is anchored by actual simulations and which part is extrapolation. At minimum, the figures should mark the extrapolated region of parameter space, and the text should state how much of the reported bound lies outside the simulation grid.

minor comments (5)

[Section IV.B] There is a typo in 'Markov hain Monte Carlo' that should read 'Markov chain Monte Carlo.'
[Section III, Eq. (26)] The integral expression contains an unexplained factor 'sqrt(i)' in the elliptic-integral term; this may be a typographical artifact, but it should be clarified or corrected.
[Section III, Fig. 3 caption] The caption reads '1 > a_D > a_D,2', which appears to be a typo; it should presumably be 'a_D,1 < a_D < a_D,2'.
[Section II.A] The sentence 'We will see in Section IV that restrictions from small-scale structure on the parameter space of gamma_D and T_RH provide much stronger bounds' is followed by a period missing after 'relic abundance'; the text should be punctuated consistently.
[Section IV.B, Eq. (35)] Equation (35) gives alpha in units of Mpc/h but the numerical coefficient is written as 0.177 (lambda_fs/Mpc)^0.908 Mpc/h; it would be clearer to state explicitly that lambda_fs is in Mpc and alpha in Mpc/h.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the velocity-distribution and free-streaming calculations are self-contained, and the external Lyman-alpha and Milky Way satellite constraints are independent of the paper's assumptions.

full rationale

The paper's central derivation in Sections II and III computes the dark matter birth-time distribution from the scalar decay equations and then obtains the resulting velocity distribution and free-streaming lengths. This is a self-contained differential calculation with no input from the data it eventually constrains. The transfer functions are generated with CLASS from the model's own distribution function, and the fitting form Eq. (34) with beta and gamma as functions of alpha is a descriptive parametrization of the model's own transfer functions, not a parameter fitted to external data. The Lyman-alpha bounds alpha < 0.011 Mpc/h and alpha < 0.026 Mpc/h are obtained by inserting this model's transfer-function family into a pre-existing MCMC likelihood from Ref. [67], which is based on independent MIKE/HIRES quasar data and precomputed hydrodynamic simulations; the Milky Way satellite bound is imported from Ref. [58]'s independent analysis. Although Refs. [66] and [67] include coauthor Murgia, they are published, externally calibrated analyses using independent data sets and simulation grids, so they count as real evidence rather than circular self-citation under the review rules. The main legitimate concern is that the Ref. [67] likelihood template is linearly extrapolated to beta and gamma values far from thermal WDM (gamma approximately -1.1 versus -4.46), and the paper explicitly acknowledges this extrapolation. That is a validation and correctness risk, not circularity by construction, because the resulting bounds are not algebraic functions of the paper's own fitted parameters. No step in the derivation reduces to its inputs, so the circularity score is 0.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The model uses a standard oscillating scalar field as the parent and standard dark matter as the daughter; no new particle, force, or conserved quantity is introduced. The free parameters are the transfer-function cutoff alpha and its auxiliary shape parameters. The main assumptions are the monochromatic two-body decay kinematics, the absence of scattering and annihilations, entropy conservation after reheating, and the transferability of WDM-based Lyman-alpha and Milky Way satellite bounds to this nonthermal model.

free parameters (2)

alpha (transfer function cutoff) = alpha < 0.011 Mpc/h (68% C.L.), < 0.026 Mpc/h (95% C.L.)
The scale of the small-scale cutoff in the nonthermal transfer function is the only free parameter in the Lyman-alpha MCMC; beta and gamma are derived as functions of alpha in Fig. 11.
beta and gamma (shape parameters) = beta = 0.0029 ln(alpha)^2 + 0.039 ln(alpha) + 2.51; gamma = -(0.0055 ln(alpha)^2 + 0.083 ln(alpha) + 1.35)
These are fit to the authors' CLASS transfer functions, but in the MCMC they are fixed functions of alpha, so they carry no independent freedom. They are auxiliary to the single constrained parameter alpha.

assumptions (5)

standard math Friedmann equations with an oscillating scalar field behaving as pressureless matter during the EMDE.
Used in Eq. (2) and the background evolution in Section II; this is standard cosmology, not introduced for this paper.
domain assumption Dark matter is produced by two-body scalar decay with one common birth velocity vD and no scattering or annihilations after production.
Stated at the start of Section II and again in the conclusions; the paper explicitly leaves momentum exchange and velocity-dependent annihilation to future work.
domain assumption Entropy is conserved after a = 3aRH, so g*S and temperature relations determine aRH/a0 and the relation between TRH and the scale factor.
Used to convert aRH to TRH in Section II and to express mu in Eq. (28).
domain assumption The WDM fitting form T(k) = [1 + (alpha k)^beta]^gamma, with beta and gamma fixed as functions of alpha, captures the nonthermal transfer function at all scales relevant to Lyman-alpha constraints.
Section IV.B, Eq. (34) and Fig. 11; the fit is performed for T(k) > 0.01 and the authors do not validate it with direct Lyman-alpha simulations of the nonthermal model.
domain assumption The WDM subhalo mass function suppression from Ref. [72] and the Milky Way satellite bound from Ref. [58] apply to this nonthermal model because its transfer function matches WDM near the half-mode scale.
Section IV.C, Eqs. (36-37); the authors note the transfer functions differ mainly at scales where T(k) is already below 0.1.

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Cite this review

Pith. "Pith review of Constraining Nonthermal Dark Matter's Impact on the Matter Power Spectrum." pith.science (2026). https://pith.science/paper/LWJAD7UQ

@misc{pith2026190810369,
  author       = {Pith},
  title        = {Pith review of: Constraining Nonthermal Dark Matter's Impact on the Matter Power Spectrum},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LWJAD7UQ}},
  note         = {Machine review of arXiv:1908.10369}
}

abstract

The inclusion of a period of (effective) matter domination following inflation and prior to the onset of radiation domination has interesting and observable consequences for structure growth. During this early matter-dominated era (EMDE), the Universe was dominated by massive particles, or an oscillating scalar field, that decayed into Standard Model particles, thus reheating the Universe. This decay process could also be the primary source of dark matter. In the absence of fine-tuning between the masses of the parent and daughter particles, both dark matter particles and Standard Model particles would be produced with relativistic velocities. We investigate the effects of the nonthermal production of dark matter particles with relativistic velocities on the matter power spectrum by determining the resulting velocity distribution function for the dark matter. We find that the vast majority of dark matter particles produced during the EMDE are still relativistic at reheating, so their free streaming erases the perturbations that grow during the EMDE. The free streaming of the dark matter particles can also prevent the formation of satellite galaxies around the Milky Way and the structures observed in the Lyman-$\alpha$ forest. For a given reheat temperature, these observations put an upper limit on the velocity of the dark matter particles at their creation. For example, for a reheat temperature of 10 MeV, dark matter must be produced with a Lorentz factor $\gamma \lesssim 550$.

Figures

Figures reproduced from arXiv: 1908.10369 by the authors.

**Figure 2.** FIG. 2: The average velocity of the dark matter particles as [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** FIG. 3: The birth time distribution function of dark mat [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: FIG. 4: Fraction of dark matter whose velocity at reheating [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 6.** Figure 6: FIG. 6: Fraction of dark matter whose free-streaming length [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 7.** Figure 7: FIG. 7: The free-streaming length of the dark matter as calcu [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

**Figure 8.** Figure 8: FIG. 8: The distribution function of dark matter for our [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

**Figure 10.** Figure 10: FIG. 10: The solid lines show the same transfer functions [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]

**Figure 11.** Figure 11: FIG. 11: The fitted values for the parameters [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]

**Figure 13.** Figure 13: FIG. 13: A plot of the relationship between the fitting pa [PITH_FULL_IMAGE:figures/full_fig_p012_13.png]

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Reference graph

Works this paper leans on

75 extracted references · 14 canonical work pages

[51]

Di Marco, G

A. Di Marco, G. Pradisi, and P. Cabella, Phys. Rev. D98, 123511 (2018), 1807.05916

arXiv 2018
[67]

Pitrou, A

C. Pitrou, A. Coc, J.-P. Uzan, and E. Vangioni, Phys. Rept. 754, 1 (2018), 1801.08023

arXiv 2018
[1]

Bertone and D

G. Bertone and D. Hooper, Rev. Mod. Phys. 90, 045002 (2018), 1605.04909

arXiv 2018
[2]

D. S. Akerib et al. (LUX), Phys. Rev. Lett. 122, 131301 (2019), 1811.11241

arXiv 2019
[3]

66 × 105Mpc ) µ  ln ( 2 T∗ Teq ) − ln  1 + √ µ 2 ( T∗ T0 ) 2 + 1     + (

work page
[4]

66 × 1011pc ) γDvD aRH a0  ln ( 2 T∗ Teq ) − ln  1 + √ ( γDvD aRH a0 ) 2( T∗ T0 ) 2 + 1     , (27) where we have used the fact that g∗ remains constant after T∗ = 2 × 10−5 GeV to set a∗T∗ = aeqTeq = a0T0. An important feature of this calculation is that the parameters of our model, the dark matter velocity at its production and the reheat temperat...

work page
[5]

The integral in Eq. (24) can be broken into three separate contributing integrals, representing the scalar- , radiation-, and matter-dominated eras (because the dark matter free-streaming length does not change signif- icantly after matter-radiation equality, we neglect dark 10-5 10-4 10-3 10-2 10-1 100 0 0.2 0.4 0.6 0.8 1 ε (λfs < λhor (aRH/10) ) vD FIG....

work page
[6]

(29) The above equation gives the scale at which the power spectrum of our model begins to diﬀer from that of the standard ΛCDM power spectrum

66 × 105Mpc ) √ T0 Teq √ 2iµ [ F ( i sinh−1√ iµ ) − F ( i sinh−1 √ iµ Teq T0 )] . (29) The above equation gives the scale at which the power spectrum of our model begins to diﬀer from that of the standard ΛCDM power spectrum. Figure 7 shows the free-streaming length calculated by Eq. (29) as a func- tion of the Lorentz factor at decay, γD, for diﬀerent va...

work page

Show all 75 references

[7]

Aprile et al

E. Aprile et al. (XENON), Phys. Rev. Lett. 121, 111302 (2018), 1805.12562

2018 arXiv
[8]

Cui et al

X. Cui et al. (PandaX-II), Phys. Rev. Lett. 119, 181302 (2017), 1708.06917

2017 arXiv
[9]

Ibarra, A

A. Ibarra, A. S. Lamperstorfer, and J. Silk, Phys. Rev. D89, 063539 (2014), 1309.2570

2014 arXiv
[10]

Ackermann et al

M. Ackermann et al. (Fermi-LAT), JCAP 1509, 008 (2015), 1501.05464

2015 arXiv
[11]

Ackermann et al

M. Ackermann et al. (Fermi-LAT), Phys. Rev. Lett. 115, 231301 (2015), 1503.02641

2015 arXiv
[12]

Liu, X.-J

W. Liu, X.-J. Bi, S.-J. Lin, and P.-F. Yin, Chin. Phys. C41, 045104 (2017), 1602.01012

2017 arXiv
[13]

Albert et al

A. Albert et al. (Fermi-LAT, DES), Astrophys. J. 834, 110 (2017), 1611.03184

2017 arXiv
[14]

Ackermann et al

M. Ackermann et al. (Fermi-LAT), Astrophys. J. 840, 43 (2017), 1704.03910

2017 arXiv
[15]

Hannestad, Phys

S. Hannestad, Phys. Rev. D70, 043506 (2004), astro- ph/0403291

2004
[16]

Kawasaki, K

M. Kawasaki, K. Kohri, and N. Sugiyama, Phys. Rev. D62, 023506 (2000), astro-ph/0002127

2000 arXiv
[17]

Ichikawa, M

K. Ichikawa, M. Kawasaki, and F. Takahashi, JCAP 0705, 007 (2007), astro-ph/0611784

2007 arXiv
[18]

Kofman, A

L. Kofman, A. D. Linde, and A. A. Starobinsky, Phys. Rev. D56, 3258 (1997), hep-ph/9704452

1997 arXiv
[19]

Allahverdi, R

R. Allahverdi, R. Brandenberger, F.-Y. Cyr-Racine, an d A. Mazumdar, Ann. Rev. Nucl. Part. Sci. 60, 27 (2010), 1001.2600

2010 arXiv
[20]

M. S. Turner, Phys. Rev. D28, 1243 (1983)

1983
[21]

Coughlan, W

G. Coughlan, W. Fischler, E. W. Kolb, S. Raby, and G. Ross, Physics Letters B 131, 59 (1983), ISSN 0370-2693, URL http://www.sciencedirect.com/science/article/pii/0370269383910912

1983
[22]

de Carlos, J

B. de Carlos, J. A. Casas, F. Quevedo, and E. Roulet, Phys. Lett. B318, 447 (1993), hep-ph/9308325

1993 arXiv
[23]

Banks, D

T. Banks, D. B. Kaplan, and A. E. Nelson, Phys. Rev. D49, 779 (1994), hep-ph/9308292

1994 arXiv
[24]

Banks, M

T. Banks, M. Berkooz, and P. J. Steinhardt, Phys. Rev. D52, 705 (1995), hep-th/9501053

1995 arXiv
[25]

Banks, M

T. Banks, M. Berkooz, S. H. Shenker, G. W. Moore, and P. J. Steinhardt, Phys. Rev. D52, 3548 (1995), hep- th/9503114

1995
[26]

B. S. Acharya, G. Kane, and E. Kuﬂik, Int. J. Mod. Phys. A29, 1450073 (2014), 1006.3272

2014 arXiv
[27]

J. T. Giblin, G. Kane, E. Nesbit, S. Watson, and Y. Zhao, Phys. Rev. D96, 043525 (2017), 1706.08536

2017 arXiv
[28]

G. Kane, K. Sinha, and S. Watson, Int. J. Mod. Phys. D24, 1530022 (2015), 1502.07746

2015 arXiv
[29]

Zhang, JCAP 1505, 008 (2015), 1502.06983

Y. Zhang, JCAP 1505, 008 (2015), 1502.06983. 15

2015 arXiv
[30]

Berlin, D

A. Berlin, D. Hooper, and G. Krnjaic, Phys. Lett. B760, 106 (2016), 1602.08490

2016 arXiv
[31]

Berlin, D

A. Berlin, D. Hooper, and G. Krnjaic, Phys. Rev. D94, 095019 (2016), 1609.02555

2016 arXiv
[32]

J. A. Dror, E. Kuﬂik, B. Melcher, and S. Watson, Phys. Rev. D97, 063524 (2018), 1711.04773

2018 arXiv
[33]

Tenkanen and V

T. Tenkanen and V. Vaskonen, Phys. Rev. D94, 083516 (2016), 1606.00192

2016 arXiv
[34]

Tenkanen (2019), 1905.11737

T. Tenkanen (2019), 1905.11737

2019 arXiv
[35]

D. J. H. Chung, E. W. Kolb, and A. Riotto, Phys. Rev. D60, 063504 (1999), hep-ph/9809453

1999 arXiv
[36]

G. F. Giudice, E. W. Kolb, and A. Riotto, Phys. Rev. D64, 023508 (2001), hep-ph/0005123

2001 arXiv
[37]

Fornengo, A

N. Fornengo, A. Riotto, and S. Scopel, Phys. Rev. D67, 023514 (2003), hep-ph/0208072

2003 arXiv
[38]

Pallis, Astropart

C. Pallis, Astropart. Phys. 21, 689 (2004), hep- ph/0402033

2004
[39]

Gelmini, P

G. Gelmini, P. Gondolo, A. Soldatenko, and C. E. Ya- guna, Phys. Rev. D74, 083514 (2006), hep-ph/0605016

2006 arXiv
[40]

G. B. Gelmini and P. Gondolo, Phys. Rev. D74, 023510 (2006), hep-ph/0602230

2006 arXiv
[41]

Roszkowski, S

L. Roszkowski, S. Trojanowski, and K. Turzy´ nski, JHEP 11, 146 (2014), 1406.0012

2014 arXiv
[42]

Drewes, JCAP 1411, 020 (2014), 1406.6243

M. Drewes, JCAP 1411, 020 (2014), 1406.6243

2014 arXiv
[43]

G. L. Kane, P. Kumar, B. D. Nelson, and B. Zheng, Phys. Rev. D93, 063527 (2016), 1502.05406

2016 arXiv
[44]

Drees and F

M. Drees and F. Hajkarim, JCAP 1802, 057 (2018), 1711.05007

2018 arXiv
[45]

Maity and P

D. Maity and P. Saha, Phys. Rev. D98, 103525 (2018), 1801.03059

2018 arXiv
[46]

Maity and P

D. Maity and P. Saha, Phys. Dark Univ. p. 100317 (2018), [Phys. Dark Univ.25,100317(2019)], 1804.10115

2018 arXiv
[47]

Bernal, C

N. Bernal, C. Cosme, and T. Tenkanen, Eur. Phys. J. C79, 99 (2019), 1803.08064

2019 arXiv
[48]

Bernal, C

N. Bernal, C. Cosme, T. Tenkanen, and V. Vaskonen, Eur. Phys. J. C79, 30 (2019), 1806.11122

2019 arXiv
[49]

Drees and F

M. Drees and F. Hajkarim, JHEP 12, 042 (2018), 1808.05706

2018 arXiv
[50]

Chowdhury, E

D. Chowdhury, E. Dudas, M. Dutra, and Y. Mambrini, Phys. Rev. D99, 095028 (2019), 1811.01947

2019 arXiv
[52]

Fan and M

J. Fan and M. Reece, JHEP 10, 124 (2013), 1307.4400

2013 arXiv
[53]

Cohen, M

T. Cohen, M. Lisanti, A. Pierce, and T. R. Slatyer, JCAP 1310, 061 (2013), 1307.4082

2013 arXiv
[54]

A. L. Erickcek and K. Sigurdson, Phys. Rev. D84, 083503 (2011), 1106.0536

2011 arXiv
[55]

J. Fan, O. ¨Ozsoy, and S. Watson, Phys. Rev. D90, 043536 (2014), 1405.7373

2014 arXiv
[56]

A. L. Erickcek, Phys. Rev. D92, 103505 (2015), 1504.03335

2015 arXiv
[57]

A. L. Erickcek, K. Sinha, and S. Watson, Phys. Rev. D94, 063502 (2016), 1510.04291

2016 arXiv
[58]

Blanco, M

C. Blanco, M. S. Delos, A. L. Erickcek, and D. Hooper (2019), 1906.00010

2019 arXiv
[60]

J. Baur, N. Palanque-Delabrouille, C. Y` eche, C. Mag- neville, and M. Viel, JCAP 1608, 012 (2016), 1512.01981

2016 arXiv
[61]

Irˇ siˇ c et al., Phys

V. Irˇ siˇ c et al., Phys. Rev. D96, 023522 (2017), 1702.01764

2017 arXiv
[62]

E. O. Nadler, V. Gluscevic, K. K. Boddy, and R. H. Wechsler, Astrophys. J. 878, L32 (2019), [Astrophys. J. Lett.878,32(2019)], 1904.10000

2019 arXiv
[63]

Jedamzik, M

K. Jedamzik, M. Lemoine, and J. Martin, JCAP 1009, 034 (2010), 1002.3039

2010 arXiv
[64]

Easther, R

R. Easther, R. Flauger, and J. B. Gilmore, JCAP 1104, 027 (2011), 1003.3011

2011 arXiv
[65]

Blackadder and S

G. Blackadder and S. M. Koushiappas, Phys. Rev. D90, 103527 (2014), 1410.0683

2014 arXiv
[66]

Aghanim et al

N. Aghanim et al. (Planck) (2018), 1807.06209

2018 arXiv
[68]

Boyarsky, J

A. Boyarsky, J. Lesgourgues, O. Ruchayskiy, and M. Viel , JCAP 0905, 012 (2009), 0812.0010

2009 arXiv
[69]

Lesgourgues and T

J. Lesgourgues and T. Tram (2015), 1104.2935

2015 arXiv
[70]

Murgia, A

R. Murgia, A. Merle, M. Viel, M. Totzauer, and A. Schneider, JCAP 1711, 046 (2017), 1704.07838

2017 arXiv
[71]

Murgia, V

R. Murgia, V. Irˇ siˇ c, and M. Viel, Phys. Rev.D98, 083540 (2018), 1806.08371

2018 arXiv
[72]

Schneider, R

A. Schneider, R. E. Smith, A. V. Macci` o, and B. Moore, MNRAS 424, 684 (2012), 1112.0330

2012 arXiv
[73]

M. Viel, G. D. Becker, J. S. Bolton, and M. G. Haehnelt, Phys. Rev. D88, 043502 (2013), 1306.2314

2013 arXiv
[74]

Archidiacono, D

M. Archidiacono, D. C. Hooper, R. Murgia, S. Bohr, J. Lesgourgues, and M. Viel (2019), 1907.01496

2019 arXiv
[75]

Murgia, G

R. Murgia, G. Scelfo, M. Viel, and A. Raccanelli, Phys. Rev. Lett. 123, 071102 (2019), 1903.10509

2019 arXiv
[76]

M. R. Lovell, C. S. Frenk, V. R. Eke, A. Jenkins, L. Gao, and T. Theuns, Mon. Not. Roy. Astron. Soc. 439, 300 (2014), 1308.1399

2014 arXiv

Pith tools

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

[1] [51]

Di Marco, G

A. Di Marco, G. Pradisi, and P. Cabella, Phys. Rev. D98, 123511 (2018), 1807.05916

arXiv 2018

[2] [67]

Pitrou, A

C. Pitrou, A. Coc, J.-P. Uzan, and E. Vangioni, Phys. Rept. 754, 1 (2018), 1801.08023

arXiv 2018

[3] [1]

Bertone and D

G. Bertone and D. Hooper, Rev. Mod. Phys. 90, 045002 (2018), 1605.04909

arXiv 2018

[4] [2]

D. S. Akerib et al. (LUX), Phys. Rev. Lett. 122, 131301 (2019), 1811.11241

arXiv 2019

[5] [3]

66 × 105Mpc ) µ  ln ( 2 T∗ Teq ) − ln  1 + √ µ 2 ( T∗ T0 ) 2 + 1     + (

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[6] [4]

66 × 1011pc ) γDvD aRH a0  ln ( 2 T∗ Teq ) − ln  1 + √ ( γDvD aRH a0 ) 2( T∗ T0 ) 2 + 1     , (27) where we have used the fact that g∗ remains constant after T∗ = 2 × 10−5 GeV to set a∗T∗ = aeqTeq = a0T0. An important feature of this calculation is that the parameters of our model, the dark matter velocity at its production and the reheat temperat...

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[7] [5]

The integral in Eq. (24) can be broken into three separate contributing integrals, representing the scalar- , radiation-, and matter-dominated eras (because the dark matter free-streaming length does not change signif- icantly after matter-radiation equality, we neglect dark 10-5 10-4 10-3 10-2 10-1 100 0 0.2 0.4 0.6 0.8 1 ε (λfs < λhor (aRH/10) ) vD FIG....

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[8] [6]

(29) The above equation gives the scale at which the power spectrum of our model begins to diﬀer from that of the standard ΛCDM power spectrum

66 × 105Mpc ) √ T0 Teq √ 2iµ [ F ( i sinh−1√ iµ ) − F ( i sinh−1 √ iµ Teq T0 )] . (29) The above equation gives the scale at which the power spectrum of our model begins to diﬀer from that of the standard ΛCDM power spectrum. Figure 7 shows the free-streaming length calculated by Eq. (29) as a func- tion of the Lorentz factor at decay, γD, for diﬀerent va...

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