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arxiv: 2605.00991 · v1 · submitted 2026-05-01 · 🌌 astro-ph.CO · hep-ph

Implications of textit{SARAS3} data for Coulomb-like interacting dark matter

Pith reviewed 2026-05-09 18:23 UTC · model grok-4.3

classification 🌌 astro-ph.CO hep-ph
keywords 21-cm signalinteracting dark matterSARAS3cosmic dawnglobal 21-cm signalBayesian analysisforeground modelingCoulomb-like interaction
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The pith

SARAS3 non-detection bounds the depth of the 21-cm absorption signal in Coulomb-like interacting dark matter models.

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

The paper examines the implications of the SARAS3 non-detection in the 55.5-84.4 MHz band for dark matter that interacts with baryons through a Coulomb-like force. The authors develop a model that self-consistently accounts for both excess gas cooling and the suppression of early structure formation, which delays star formation and weakens the associated radiation backgrounds. After performing a joint Bayesian fit of the 21-cm signal and a flexible foreground model to the data, they find that the observations rule out deep absorption troughs, with the strongest limit at redshift 23.6. This result constrains the possible amplitude of the global 21-cm signal in these models even though it does not favor interacting dark matter over standard cold dark matter.

Core claim

The SARAS3 antenna temperature data, after marginalizing over flexible foreground parameters, disfavors deep absorption in the 21-cm global signal for Coulomb-like IDM, with the strongest constraint T21 ≳ -277.6 mK at z=23.6, and yields no statistical preference for IDM over CDM as the Bayes factor is only about 1.7. While the strength of baryon-DM interactions remains unconstrained, the non-detection places a meaningful upper bound on the amplitude of the global 21-cm signal in this class of models.

What carries the argument

A self-consistent model of Coulomb-like baryon-dark matter interactions that incorporates both gas cooling and suppression of small-scale structure formation, delaying the Ly-alpha, X-ray, and ionizing backgrounds.

If this is right

  • The amplitude of the global 21-cm signal cannot exceed a depth of roughly 278 mK at z=23.6 in Coulomb-like IDM models.
  • Current SARAS3 data provides no statistically significant preference for IDM over standard cold dark matter.
  • The strength of the baryon-DM interaction itself is not constrained by this analysis.
  • The non-detection supplies a concrete upper limit on the 21-cm signal strength for this class of models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same self-consistent modeling approach could be applied to data from other 21-cm experiments to test different dark matter interaction strengths.
  • Persistent non-detections across frequency bands would imply that any IDM effects on cosmic dawn remain subtle under current modeling.
  • A positive detection of the 21-cm signal in future observations could break degeneracies and allow direct constraints on the interaction parameters.

Load-bearing premise

The chosen IDM interaction model plus the flexible foreground parametrization together capture all relevant physics and systematics in the 55.5-84.4 MHz band without residual biases from unmodeled effects.

What would settle it

A future independent measurement detecting a 21-cm absorption feature deeper than -277.6 mK at z=23.6 would contradict the SARAS3 bound under the paper's modeling assumptions.

read the original abstract

The 21-cm signal from cosmic dawn is a potentially sensitive probe of interactions between dark matter (DM) and baryons. We investigate the implications of the SARAS3 non-detection in the 55.5-84.4 MHz band for Coulomb-like interacting DM (IDM). In contrast to earlier constraint analyses that focused primarily on baryon cooling, we model the interaction self-consistently by including both excess cooling of the gas and the suppression of structure formation, which delays the onset of star formation and hence suppresses the Ly$\alpha$, X-ray, and ionizing backgrounds at early times. We perform a joint Bayesian fit of a global 21-cm signal model and a flexible foreground model to the SARAS3 antenna temperature, and find that the signal parameters remain weakly constrained after marginalizing over the foregrounds. The null result is nonetheless informative: the data disfavour deep absorption features within the observed band, with the strongest bound at $z = 23.6$ ($\nu \approx 57.7$ MHz), where $T_{21} \gtrsim -277.6$ mK at $3\sigma$. Comparing the IDM and standard cold dark matter scenarios, we find no statistically significant preference for IDM (Bayes factor $B \approx 1.7$). While we do not constrain the strength of baryon-DM interactions, the SARAS3 non-detection places a meaningful upper bound on the amplitude of the global 21-cm signal in this class of models.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates the implications of the SARAS3 non-detection in the 55.5-84.4 MHz band for Coulomb-like interacting dark matter (IDM). It models the interactions self-consistently by including both excess baryon cooling and suppression of structure formation (which delays star formation and suppresses Lyα, X-ray, and ionizing backgrounds). A joint Bayesian fit of the global 21-cm signal model and a flexible foreground model is performed on the SARAS3 antenna temperature data. The signal parameters remain weakly constrained after foreground marginalization, but the data disfavors deep absorption, with the strongest 3σ bound T_{21} ≳ -277.6 mK at z=23.6. No statistically significant preference for IDM over CDM is found (Bayes factor B ≈ 1.7).

Significance. If the modeling assumptions hold, this provides a meaningful upper bound on the amplitude of the global 21-cm absorption signal in the observed band for this class of IDM models. The self-consistent inclusion of structure suppression alongside cooling is a clear strength relative to earlier analyses focused primarily on cooling. The honest reporting of weak constraints on signal parameters after marginalization over foregrounds, rather than overstated limits, is also positive and contributes to careful use of 21-cm data for DM constraints.

major comments (2)
  1. [§4.1] §4.1 (reporting the 3σ bound): The central claim that the SARAS3 non-detection disfavors deep absorption features (strongest at z=23.6 with T_{21} ≳ -277.6 mK) rests on the joint posterior after foreground marginalization. However, the manuscript does not present recovery tests on mock data sets that inject signals with additional unmodeled effects such as inhomogeneous X-ray heating or extra astrophysical Lyα sources. These could independently alter spin-temperature evolution and allow deeper absorption to remain consistent with the data, directly affecting the robustness of the reported bound.
  2. [§4.3] §4.3 (Bayes factor): The reported Bayes factor B ≈ 1.7 showing no significant preference for IDM over CDM is a key comparative result. Details on the prior range adopted for the IDM interaction strength and the numerical settings used to compute the Bayesian evidence (e.g., nested sampling parameters) are not provided, preventing assessment of whether the evidence ratio is stable under reasonable variations in these choices.
minor comments (2)
  1. [Abstract and title] The abstract and title use slightly inconsistent phrasing for the model ('Coulomb-like interacting DM (IDM)' vs. 'Coulomb-like interacting dark matter'); standardizing the introduction of the acronym would improve clarity.
  2. [Throughout] Notation for the 21-cm brightness temperature fluctuates between T21 and T_{21} in the text; consistent use of math mode throughout would enhance readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. We address each of the major comments below and have updated the manuscript accordingly to improve clarity and completeness.

read point-by-point responses
  1. Referee: [§4.1] The central claim that the SARAS3 non-detection disfavors deep absorption features (strongest at z=23.6 with T_{21} ≳ -277.6 mK) rests on the joint posterior after foreground marginalization. However, the manuscript does not present recovery tests on mock data sets that inject signals with additional unmodeled effects such as inhomogeneous X-ray heating or extra astrophysical Lyα sources. These could independently alter spin-temperature evolution and allow deeper absorption to remain consistent with the data, directly affecting the robustness of the reported bound.

    Authors: We thank the referee for pointing out this potential limitation in assessing the robustness of our 3σ bound. Our analysis is based on a self-consistent IDM model that accounts for both enhanced baryon cooling and delayed structure formation affecting the radiation backgrounds. We did not include recovery tests with additional unmodeled effects like inhomogeneous X-ray heating or extra Lyα sources, as these would require extensions beyond our current modeling framework. In the revised manuscript, we have added a discussion in §4.1 noting this caveat and clarifying that the bound applies under the assumptions of the global 21-cm signal model used. This maintains the honest reporting of the constraints without overstating their generality. revision: partial

  2. Referee: [§4.3] The reported Bayes factor B ≈ 1.7 showing no significant preference for IDM over CDM is a key comparative result. Details on the prior range adopted for the IDM interaction strength and the numerical settings used to compute the Bayesian evidence (e.g., nested sampling parameters) are not provided, preventing assessment of whether the evidence ratio is stable under reasonable variations in these choices.

    Authors: We agree that these details are essential for reproducibility and to evaluate the stability of the Bayes factor. We have revised the manuscript to include the prior range for the IDM interaction strength and the specific numerical settings for the nested sampling computation of the Bayesian evidence, including live points and convergence criteria. Furthermore, we performed additional checks by adjusting the prior ranges and found the Bayes factor to be stable at approximately 1.7. These updates are incorporated in §4.3 and the methods section. revision: yes

Circularity Check

0 steps flagged

No significant circularity in Bayesian fit to SARAS3 data

full rationale

The paper performs a joint Bayesian likelihood analysis fitting an IDM global 21-cm signal model (with self-consistent baryon cooling plus structure-formation suppression) and a flexible foreground parametrization directly to the SARAS3 antenna-temperature measurements in the 55.5-84.4 MHz band. The reported 3σ bound T21 ≳ -277.6 mK at z=23.6 and the Bayes factor B≈1.7 are direct outputs of this marginalization over nuisance parameters; they are not obtained by renaming or re-deriving any fitted quantity as an independent prediction. No self-definitional steps, fitted-input-as-prediction reductions, or load-bearing self-citations appear in the derivation chain. The modeling choices are explicit inputs to the fit rather than outputs derived from the data by construction. The result is therefore self-contained against the external observational dataset.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard 21-cm radiative transfer, the validity of the chosen IDM interaction cross-section scaling, and the assumption that foregrounds can be parametrized flexibly without absorbing the signal. No new particles or forces are invented; the interaction strength itself is not constrained.

free parameters (3)
  • IDM interaction strength
    Not constrained by the data; treated as a free parameter whose effects are explored but not fitted to a specific value.
  • Foreground model coefficients
    Flexible parametrization marginalized over in the Bayesian fit; their exact number and functional form are not stated in the abstract.
  • Signal amplitude and timing parameters
    Fitted jointly with foregrounds; the reported bound is on the marginal posterior of the absorption depth.
axioms (2)
  • standard math Standard ΛCDM background cosmology and linear perturbation theory for structure growth
    Invoked when modeling the delay in star formation due to suppressed small-scale power.
  • domain assumption 21-cm brightness temperature formula depends only on gas kinetic temperature, spin temperature, and neutral fraction
    Used to translate IDM cooling and delayed star formation into a global signal.

pith-pipeline@v0.9.0 · 5583 in / 1678 out tokens · 53673 ms · 2026-05-09T18:23:02.638180+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

108 extracted references · 5 canonical work pages

  1. [1]

    Rubin and J

    V.C. Rubin and J. Ford, W. Kent,Rotation of the Andromeda Nebula from a Spectroscopic Survey of Emission Regions,Astrophys. J.159(1970) 379

  2. [2]

    van Albada, J.N

    T.S. van Albada, J.N. Bahcall, K. Begeman and R. Sancisi,Distribution of dark matter in the spiral galaxy NGC 3198.,Astrophys. J.295(1985) 305

  3. [3]

    Trimble,Existence and nature of dark matter in the universe,Annu

    V. Trimble,Existence and nature of dark matter in the universe,Annu. Rev. Astron. Astrophys.25(1987) 425

  4. [4]

    Clowe, M

    D. Clowe, M. Bradač, A.H. Gonzalez, M. Markevitch, S.W. Randall, C. Jones et al.,A direct empirical proof of the existence of dark matter,Astrophys. J.648(2006) L109

  5. [5]

    Peebles,The Large-Scale Structure of the Universe, Princeton University Press (1980)

    P.J.E. Peebles,The Large-Scale Structure of the Universe, Princeton University Press (1980)

  6. [6]

    Peacock, S

    J.A. Peacock, S. Cole, P. Norberg, C.M. Baugh, J. Bland-Hawthorn, T. Bridges et al.,A measurement of the cosmological mass density from clustering in the 2dF Galaxy Redshift Survey,Nature410(2001) 169

  7. [7]

    Massey, J

    R. Massey, J. Rhodes, R. Ellis, N. Scoville, A. Leauthaud, A. Finoguenov et al.,Dark matter maps reveal cosmic scaffolding,Nature445(2007) 286

  8. [8]

    Chan,Two mysterious universal dark matter–baryon relations in galaxies and galaxy clusters,Phys

    M.H. Chan,Two mysterious universal dark matter–baryon relations in galaxies and galaxy clusters,Phys. Dark Universe38(2022) 101142

  9. [9]

    Salucci, M.I

    P. Salucci, M.I. Wilkinson, M.G. Walker, G.F. Gilmore, E.K. Grebel, A. Koch et al.,Dwarf spheroidal galaxy kinematics and spiral galaxy scaling laws,Mon. Not. R. Astron. Soc.420 (2012) 2034

  10. [10]

    too big to fail

    E. Papastergis, R. Giovanelli, M.P. Haynes and F. Shankar,Is there a “too big to fail” problem in the field?,Astron. Astrophys.574(2015) A113

  11. [11]

    Oman, J.F

    K.A. Oman, J.F. Navarro, A. Fattahi, C.S. Frenk, T. Sawala, S.D.M. White et al.,The unexpected diversity of dwarf galaxy rotation curves,Mon. Not. R. Astron. Soc.452(2015) 3650

  12. [12]

    Adriani, G.C

    O. Adriani, G.C. Barbarino, G.A. Bazilevskaya, R. Bellotti, M. Boezio, E.A. Bogomolov et al.,An anomalous positron abundance in cosmic rays with energies 1.5–100 gev,Nature 458(2009) 607

  13. [13]

    Weniger,A tentative gamma-ray line from dark matter annihilation at the fermi large area telescope,J

    C. Weniger,A tentative gamma-ray line from dark matter annihilation at the fermi large area telescope,J. Cosmo. Astropart. Phys.2012(2012) 007

  14. [14]

    Spergel and P.J

    D.N. Spergel and P.J. Steinhardt,Observational evidence for self-interacting cold dark matter, Phys. Rev. Lett.84(2000) 3760

  15. [15]

    Feng,Dark matter candidates from particle physics and methods of detection,Annu

    J.L. Feng,Dark matter candidates from particle physics and methods of detection,Annu. Rev. Astron. Astrophys.48(2010) 495

  16. [16]

    Buen-Abad, R

    M.A. Buen-Abad, R. Essig, D. McKeen and Y.-M. Zhong,Cosmological constraints on dark matter interactions with ordinary matter,Phys. Rep.961(2022) 1

  17. [17]

    Slatyer,What does cosmology teach us about non-gravitational properties of dark matter?,Nuc

    T.R. Slatyer,What does cosmology teach us about non-gravitational properties of dark matter?,Nuc. Phys. B1003(2024) 116468. – 20 –

  18. [18]

    Bergström,Dark matter candidates,New J

    L. Bergström,Dark matter candidates,New J. Phys.11(2009) 105006

  19. [19]

    Bertone and D

    G. Bertone and D. Hooper,History of dark matter,Rev. Mod. Phys.90(2018) 045002

  20. [20]

    Arbey and F

    A. Arbey and F. Mahmoudi,Dark matter and the early universe: A review,Prog. Part. Nucl. Phys.119(2021) 103865

  21. [21]

    Muñoz, E.D

    J.B. Muñoz, E.D. Kovetz and Y. Ali-Haïmoud,Heating of baryons due to scattering with dark matter during the dark ages,Phys. Rev. D92(2015) 083528

  22. [22]

    Sigurdson, M

    K. Sigurdson, M. Doran, A. Kurylov, R.R. Caldwell and M. Kamionkowski,Dark-matter electric and magnetic dipole moments,Phys. Rev. D70(2004) 083501

  23. [23]

    Dubovsky, D.S

    S.L. Dubovsky, D.S. Gorbunov and G.I. Rubtsov,Narrowing the window for millicharged particles by cmb anisotropy,J. Exp. Theor. Phys.79(2004) 1

  24. [24]

    Davidson, S

    S. Davidson, S. Hannestad and G. Raffelt,Updated bounds on milli-charged particles,J. High Energy Phys.2000(2000) 003

  25. [25]

    Dvorkin, K

    C. Dvorkin, K. Blum and M. Kamionkowski,Constraining dark matter-baryon scattering with linear cosmology,Phy. Rev. D89(2014) 023519

  26. [26]

    Turner,The dark side of the universe: from zwicky to accelerated expansion,Phys

    M.S. Turner,The dark side of the universe: from zwicky to accelerated expansion,Phys. Rep. 333-334(2000) 619

  27. [27]

    Seager, D

    S. Seager, D. Sasselov and D. Scott,A New Calculation of the Recombination Epoch, Astrophys. J.523(1999) L1

  28. [28]

    Seager, D.D

    S. Seager, D.D. Sasselov and D. Scott,How Exactly Did the Universe Become Neutral?, Astrophys. J. Suppl. Ser.128(2000) 407

  29. [29]

    Madau, A

    P. Madau, A. Meiksin and M.J. Rees,21 centimeter tomography of the intergalactic medium at high redshift,Astrophys. J.475(1997) 429

  30. [30]

    Furlanetto, S

    S.R. Furlanetto, S. Peng Oh and F.H. Briggs,Cosmology at low frequencies: The 21 cm transition and the high-redshift universe,Phys. Rep.433(2006) 181

  31. [31]

    Pritchard and A

    J.R. Pritchard and A. Loeb,21 cm cosmology in the 21st century,Rep. Prog. Phys.75(2012) 086901

  32. [32]

    O.Z. Katz, N. Outmezguine, D. Redigolo and T. Volansky,Probing new physics at cosmic dawn with 21-cm cosmology,Nucl. Phys. B1003(2024) 116502

  33. [33]

    Condon,Radio emission from normal galaxies,Annu

    J.J. Condon,Radio emission from normal galaxies,Annu. Rev. Astron. Astrophys.30(1992) 575

  34. [34]

    Mittal, G

    S. Mittal, G. Kulkarni, D. Anstey and E. de Lera Acedo,Impact of extragalactic point sources on the low-frequency sky spectrum and cosmic dawn global 21-cm measurements,Mon. Not. R. Astron. Soc.534(2024) 1317

  35. [35]

    Scheutwinkel, E

    K.H. Scheutwinkel, E. de Lera Acedo and W. Handley,Bayesian evidence-driven diagnosis of instrumental systematics for sky-averaged 21-cm cosmology experiments,Publ. Astron. Soc. Aust.39(2022) e052

  36. [36]

    Tripathi, A

    A. Tripathi, A. Datta, M. Choudhury and S. Majumdar,Extracting the Global 21-cm signal from Cosmic Dawn and Epoch of Reionization in the presence of Foreground and Ionosphere, Mon. Not. R. Astron. Soc.528(2024) 1945

  37. [37]

    Bowman, A.E.E

    J.D. Bowman, A.E.E. Rogers, R.A. Monsalve, T.J. Mozdzen and N. Mahesh,An absorption profile centred at 78 megahertz in the sky-averaged spectrum,Nature555(2018) 67

  38. [38]

    Hills, G

    R. Hills, G. Kulkarni, P.D. Meerburg and E. Puchwein,Concerns about modelling of the EDGES data,Nature564(2018) E32

  39. [39]

    Singh and R

    S. Singh and R. Subrahmanyan,The Redshifted 21 cm Signal in the EDGES Low-band Spectrum,Astrophys. J.880(2019) 26. – 21 –

  40. [40]

    Bradley, K

    R.F. Bradley, K. Tauscher, D. Rapetti and J.O. Burns,A Ground Plane Artifact that Induces an Absorption Profile in Averaged Spectra from Global 21 cm Measurements, with Possible Application to EDGES,Astrophys. J.874(2019) 153

  41. [41]

    Sims and J.C

    P.H. Sims and J.C. Pober,Testing for calibration systematics in the edges low-band data using bayesian model selection,Mon. Not. R. Astron. Soc.492(2019) 22

  42. [42]

    L. Xiao, R. An, L. Zhang, B. Yue, Y. Xu and B. Wang,Can conformal and disformal couplings between dark sectors explain the edges 21-cm anomaly?,Phys. Rev. D99(2019) 023528

  43. [43]

    Mukhopadhyay, D

    U. Mukhopadhyay, D. Majumdar and K.K. Datta,Probing interacting dark energy and scattering of baryons with dark matter in light of the edges 21-cm signal,Phys. Rev. D103 (2021) 063510

  44. [44]

    Dhuria, V

    M. Dhuria, V. Karambelkar, V. Rentala and P. Sarmah,A strong broadband 21 cm cosmological signal from dark matter spin-flip interactions,J. Cosmo. Astropart. Phys.2021 (2021) 041

  45. [45]

    Mathur, S

    A. Mathur, S. Rajendran and H. Ramani,Composite solution to the edges anomaly,Phys. Rev. D105(2022) 075020

  46. [46]

    Mittal and G

    S. Mittal and G. Kulkarni,Implications of the cosmological 21-cm absorption profile for high-redshift star formation and deep JWST surveys,Mon. Not. R. Astron. Soc.515(2022) 2901

  47. [47]

    Barkana,Possible interaction between baryons and dark-matter particles revealed by the first stars,Nature555(2018) 71

    R. Barkana,Possible interaction between baryons and dark-matter particles revealed by the first stars,Nature555(2018) 71

  48. [48]

    Berlin, D

    A. Berlin, D. Hooper, G. Krnjaic and S.D. McDermott,Severely constraining dark-matter interpretations of the 21-cm anomaly,Phys. Rev. Lett.121(2018) 011102

  49. [49]

    Fialkov, R

    A. Fialkov, R. Barkana and A. Cohen,Constraining baryon–dark-matter scattering with the cosmic dawn 21-cm signal,Phys. Rev. Lett.121(2018) 011101

  50. [50]

    Liu, N.J

    H. Liu, N.J. Outmezguine, D. Redigolo and T. Volansky,Reviving millicharged dark matter for 21-cm cosmology,Phys. Rev. D100(2019) 123011

  51. [51]

    Barkana, N.J

    R. Barkana, N.J. Outmezguine, D. Redigolo and T. Volansky,Strong constraints on light dark matter interpretation of the EDGES signal,Phys. Rev. D98(2018) 103005

  52. [52]

    Thekkeppattu, R

    J.N. Thekkeppattu, R. Subrahmanyan, R. Somashekar, N.U. Shankar, S. Singh, A. Raghunathan et al.,SARAS 3 CD/EoR radiometer: design and performance of the receiver,Exp. Astron.51(2021) 193

  53. [53]

    Singh, J

    S. Singh, J. Nambissan T., R. Subrahmanyan, N. Udaya Shankar, B.S. Girish, A. Raghunathan et al.,On the detection of a cosmic dawn signal in the radio background, Nature6(2022) 607

  54. [54]

    de Lera Acedo, D.I.L

    E. de Lera Acedo, D.I.L. de Villiers, N. Razavi-Ghods, W. Handley, A. Fialkov, A. Magro et al.,The REACH radiometer for detecting the 21-cm hydrogen signal from redshift z≈7.5–28,Nat. Astron.6(2022) 984

  55. [55]

    Driskell, E.O

    T. Driskell, E.O. Nadler, J. Mirocha, A. Benson, K.K. Boddy, T.D. Morton et al.,Structure formation and the global 21-cm signal in the presence of coulomb-like dark matter-baryon interactions,Phys. Rev. D106(2022) 103525

  56. [56]

    Rahimieh, P

    A. Rahimieh, P. Parashari, R. An, T. Driskell, J. Mirocha and V. Gluscevic,Sensitivity of the Global 21-cm Signal to Dark Matter-Baryon Scattering,arXiv e-prints(2025) arXiv:2505.03148 [2505.03148]

  57. [57]

    Rahimieh, P

    A. Rahimieh, P. Parashari and V. Gluscevic,Forecasting 21-cm power spectrum sensitivity to dark matter–baryon scattering,Mon. Not. R. Astron. Soc.542(2025) 1605. – 22 –

  58. [58]

    Fixsen,The Temperature of the Cosmic Microwave Background,Astrophys

    D.J. Fixsen,The Temperature of the Cosmic Microwave Background,Astrophys. J.707 (2009) 916

  59. [59]

    Aghanim, Y

    N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini et al., Planck 2018 results - VI. Cosmological parameters,Astron. Astrophys.641(2020) A6

  60. [60]

    Mittal, G

    S. Mittal, G. Kulkarni and P. Sims,ECHO21: a tool for modelling global 21-cm signal from dark ages to reionization,RAS Tech. Instrum.5(2026) rzag001

  61. [61]

    Mittal, A

    S. Mittal, A. Ray, G. Kulkarni and B. Dasgupta,Constraining primordial black holes as dark matter using the global 21-cm signal with x-ray heating and excess radio background,J. Cosmol. Astropart. Phys.2022(2022) 030

  62. [62]

    Mittal and G

    S. Mittal and G. Kulkarni,Lyαcoupling and heating at cosmic dawn,Mon. Not. R. Astron. Soc.503(2020) 4264

  63. [63]

    Fialkov and R

    A. Fialkov and R. Barkana,Signature of excess radio background in the 21-cm global signal and power spectrum,Mon. Not. R. Astron. Soc.486(2019) 1763

  64. [64]

    Mittal and G

    S. Mittal and G. Kulkarni,Background of radio photons from primordial black holes,Mon. Not. R. Astron. Soc.510(2022) 4992

  65. [65]

    Barkana and A

    R. Barkana and A. Loeb,Detecting the earliest galaxies through two new sources of 21 centimeter fluctuations,Astrophys. J.626(2005) 1

  66. [66]

    I. Reis, A. Fialkov and R. Barkana,The subtlety of Lyαphotons: changing the expected range of the 21-cm signal,Mon. Not. R. Astron. Soc.506(2021) 5479

  67. [67]

    Semelin, R

    B. Semelin, R. Mériot, F. Mertens, L.V.E. Koopmans, D. Aubert, R. Barkana et al.,Accurate modelling of the Lyman-pling for the 21-cm signal, observability with NenuFAR, and SKA, Astron. Astrophys.672(2023) A162

  68. [68]

    Mittal, G

    S. Mittal, G. Kulkarni and T. Garel,Radiative transfer of Lyman-αphotons at cosmic dawn with realistic gas physics,Mon. Not. R. Astron. Soc.534(2024) 1317

  69. [69]

    Flitter, J.B

    J. Flitter, J.B. Muñoz and A. Mesinger,Semi-analytical approach to Lyαmultiple-scattering in 21-cm signal simulations,arXiv e-prints(2026) arXiv:2601.14360 [2601.14360]

  70. [70]

    Ali-Haïmoud and C.M

    Y. Ali-Haïmoud and C.M. Hirata,Ultrafast effective multilevel atom method for primordial hydrogen recombination,Phys. Rev. D82(2010) 063521

  71. [71]

    Chluba and R.M

    J. Chluba and R.M. Thomas,Towards a complete treatment of the cosmological recombination problem,Mon. Not. R. Astron. Soc.412(2011) 748

  72. [72]

    Chluba, D

    J. Chluba, D. Paoletti, F. Finelli and J.A. Rubiño-Martín,Effect of primordial magnetic fields on the ionization history,Mon. Not. R. Astron. Soc.451(2015) 2244

  73. [73]

    Weymann,Diffusion Approximation for a Photon Gas Interacting with a Plasma via the Compton Effect,Phys

    R. Weymann,Diffusion Approximation for a Photon Gas Interacting with a Plasma via the Compton Effect,Phys. Fluids8(1965) 2112

  74. [74]

    Mirocha and S.R

    J. Mirocha and S.R. Furlanetto,What does the first highly redshifted 21-cm detection tell us about early galaxies?,Mon. Not. R. Astron. Soc.483(2019) 1980

  75. [75]

    Furlanetto,The global 21-centimeter background from high redshifts,Mon

    S.R. Furlanetto,The global 21-centimeter background from high redshifts,Mon. Not. R. Astron. Soc.371(2006) 867

  76. [76]

    Lehmer, E.B

    B.D. Lehmer, E.B. Monson, R.T. Eufrasio, A. Amiri, K. Doore, A. Basu-Zych et al.,An empirical framework characterizing the metallicity and star-formation history dependence of x-ray binary population formation and emission in galaxies,Astrophys. J.977(2024) 189

  77. [77]

    Mesinger, S

    A. Mesinger, S. Furlanetto and R. Cen,21CMFAST: a fast, seminumerical simulation of the high-redshift 21-cm signal,Mon. Not. R. Astron. Soc.411(2011) 955

  78. [78]

    Shull and M

    J. Shull and M. van Steenberg,X-ray secondary heating and ionization in quasar emission-line clouds,Astrophys. J.298(1985) 268. – 23 –

  79. [79]

    Madau, F

    P. Madau, F. Haardt and M.J. Rees,Radiative Transfer in a Clumpy Universe. III. The Nature of Cosmological Ionizing Sources,Astrophys. J.514(1999) 648

  80. [80]

    Shull, A

    J.M. Shull, A. Harness, M. Trenti and B.D. Smith,Critical star formation rates for reionization: Full reionization occurs at redshiftz≈7,Astrophys. J.747(2012) 100

Showing first 80 references.