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arxiv: 2605.18301 · v1 · pith:HHKSODE2new · submitted 2026-05-18 · 🌌 astro-ph.CO

Probing Reionization up to the Mark: The Marked Power Spectrum to unveil the HI 21-cm signal from the EoR

Vishrut Pandya , Leon Noble , Suman Majumdar , Debanjan Sarkar , Mohd Kamran , Abhirup Datta This is my paper

Pith reviewed 2026-05-20 00:13 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords Epoch of Reionization21-cm signalMarked power spectrumNon-Gaussian statisticsIntergalactic mediumHI brightness temperatureFisher matrix
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The pith

Marked power spectra extract additional non-Gaussian information from the 21-cm signal during reionization.

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

The paper applies marked statistics to the redshifted 21-cm brightness temperature field from neutral hydrogen in the intergalactic medium. It introduces mark functions tailored to the Epoch of Reionization and computes both the power spectrum of the marked field and the power spectrum of the mark itself. These choices let the analysis emphasize signals from different ionized and neutral environments while recovering extra information that the standard power spectrum misses. A reader would care because the method offers a simpler computational route than bispectra for tightening constraints on reionization models from future radio observations.

Core claim

Using semi-numerical 21-cm simulations, the authors show that suitably chosen EoR-tailored marks selectively enhance contributions from different IGM environments, capture non-Gaussian information beyond the standard power spectrum, and improve the statistical constraining power on EoR model parameters when evaluated in a Fisher-matrix analysis.

What carries the argument

EoR-tailored mark functions applied to the 21-cm brightness-temperature field, which weight the map to highlight specific ionized or neutral regions before power spectra are computed.

If this is right

  • Marked statistics recover part of the non-Gaussian information that the standard power spectrum loses during the EoR.
  • They improve the precision of constraints on EoR model parameters in a Fisher-matrix forecast.
  • Different mark choices can be tuned to emphasize signals from ionized bubbles versus neutral patches.
  • Both the marked-field power spectrum and the mark power spectrum function as practical extensions of two-point statistics.

Where Pith is reading between the lines

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

  • These marks could be applied directly to upcoming SKA or HERA data to extract more astrophysical information without requiring full higher-order statistics.
  • Optimizing mark functions for specific questions such as bubble-size distributions might further reduce parameter degeneracies.
  • The approach might combine naturally with other 21-cm summary statistics to cross-check reionization timelines.

Load-bearing premise

The semi-numerical 21-cm simulations used faithfully reproduce the complex growth and morphology of ionized regions in the real intergalactic medium.

What would settle it

A comparison showing that marked power spectra computed from these simulations differ substantially from those measured in full radiative-transfer simulations or in actual 21-cm observations from telescopes would falsify the improvement in constraints.

read the original abstract

The redshifted 21-cm signal from neutral hydrogen (HI) in the intergalactic medium (IGM) is a powerful probe of the Epoch of Reionization (EoR). Owing to the complex growth and morphology of ionized regions, the 21-cm brightness-temperature field becomes strongly non-Gaussian during the EoR, limiting the information captured by the standard power spectrum alone. While higher-order statistics such as the bispectrum can recover part of this information, they are computationally expensive and often less straightforward to interpret. In this work, we investigate marked statistics as an alternative framework for characterizing the EoR 21-cm signal. Using semi-numerical 21-cm simulations, we introduce a set of EoR-tailored mark functions, inspired by and extending existing marked-statistics ideas, and study both the power spectrum of the mark and that of the marked field. We show that suitably chosen marks can selectively enhance contributions from different IGM environments, capture additional non-Gaussian information beyond the standard power spectrum, and improve the statistical constraining power on EoR model parameters in a Fisher-matrix analysis. These results demonstrate that Fourier-space marked statistics, including both the power spectrum of the mark and that of the marked field, provide a computationally simple and flexible extension of standard two-point statistics for extracting astrophysical information from the EoR 21-cm signal.

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 paper investigates marked statistics as a tool to analyze the non-Gaussian 21-cm brightness-temperature field during the Epoch of Reionization. Using semi-numerical simulations, the authors introduce EoR-tailored mark functions and compute both the power spectrum of the mark and the marked field. They show that suitable marks can weight different IGM environments, recover additional information beyond the standard power spectrum, and improve Fisher-matrix constraints on reionization model parameters.

Significance. If the reported gains hold under more complete physics, the method would supply a computationally lightweight extension of two-point statistics that could tighten astrophysical constraints from SKA and similar arrays. The simulation-based tests and explicit Fisher comparison provide a reproducible framework for quantifying the improvement, though the absence of machine-checked derivations or parameter-free predictions keeps the result at the level of a promising numerical demonstration rather than a definitive theoretical advance.

major comments (2)
  1. [§4.3, Eq. (12)] §4.3 and Eq. (12): the Fisher-matrix improvement is demonstrated exclusively inside the excursion-set ionization fields of the semi-numerical code; a mismatch in bubble-size distribution or topology (as expected from full RT+hydro) would change which regions the marks weight and could erase the reported gain in parameter constraints.
  2. [§3.1] §3.1: the mark functions are constructed to enhance specific IGM environments identified in the same simulations used for the Fisher forecast; without an independent validation set or analytic derivation, it remains unclear whether the extra non-Gaussian information is robust or an artifact of the simulation assumptions.
minor comments (2)
  1. [Figure 3] Figure 3: the error bars on the marked power spectra are not described in the caption; it is unclear whether they represent sample variance, thermal noise, or both.
  2. [Abstract] The abstract states that marks 'capture additional non-Gaussian information,' but the text does not quantify the overlap with the bispectrum on the same fields; a brief comparison would strengthen the claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. The comments correctly identify key limitations arising from our use of semi-numerical simulations. We address each major comment below and have revised the manuscript to include additional discussion of these caveats while maintaining that the reported results constitute a useful demonstration of the method.

read point-by-point responses

  1. Referee: [§4.3, Eq. (12)] §4.3 and Eq. (12): the Fisher-matrix improvement is demonstrated exclusively inside the excursion-set ionization fields of the semi-numerical code; a mismatch in bubble-size distribution or topology (as expected from full RT+hydro) would change which regions the marks weight and could erase the reported gain in parameter constraints.

    Authors: We agree that the quantitative gains are shown within the specific ionization morphology produced by the excursion-set formalism. Full radiation-hydrodynamics simulations can generate different bubble-size distributions and topologies, which could alter the regions preferentially weighted by the marks and thereby modify the improvement in Fisher constraints. Semi-numerical codes remain the standard tool for exploring large parameter spaces in EoR studies, and the marked-statistics framework itself is not tied to any particular simulation method. In the revised manuscript we expand the discussion around Eq. (12) and in the conclusions to explicitly state this limitation and to recommend validation with more complete simulations as future work. revision: partial

  2. Referee: [§3.1] §3.1: the mark functions are constructed to enhance specific IGM environments identified in the same simulations used for the Fisher forecast; without an independent validation set or analytic derivation, it remains unclear whether the extra non-Gaussian information is robust or an artifact of the simulation assumptions.

    Authors: The functional forms of the marks were chosen on physical grounds to emphasize under-dense neutral regions, over-dense neutral regions, and ionized bubbles, respectively. The specific numerical parameters were then tuned on the simulation suite. While this procedure is common in exploratory analyses, we acknowledge the absence of an independent validation set or fully analytic derivation. In the revised Section 3.1 we provide a more explicit physical motivation for each mark and add a short robustness test using a second, independently generated simulation realization with altered reionization parameters. We maintain that the improvement is not an artifact, because the same marks yield consistent gains across the full set of reionization parameters examined. revision: partial

Circularity Check

0 steps flagged

No circularity: numerical demonstration on independent semi-numerical simulations

full rationale

The paper introduces EoR-tailored mark functions (inspired by prior marked-statistics literature) and applies them inside semi-numerical 21-cm simulations to compute marked power spectra and perform a standard Fisher-matrix forecast. The claimed improvements in non-Gaussian information capture and parameter constraints are shown numerically within those simulations rather than derived by algebraic reduction to the input definitions or by fitting a parameter on a subset and relabeling the output as a prediction. No self-citation load-bearing steps, uniqueness theorems imported from the same authors, or ansatz smuggling appear in the derivation chain. The analysis is self-contained against external benchmarks once the simulation suite and Fisher formalism are accepted; the weakest link is the fidelity of the semi-numerical ionization morphology, which is an assumption about physical realism rather than a circularity in the statistical pipeline.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on the accuracy of the semi-numerical simulations for modeling IGM ionization morphology and on the appropriateness of the chosen mark functions for highlighting relevant environments.

axioms (1)
  • domain assumption Semi-numerical simulations accurately reproduce the non-Gaussian morphology and growth of ionized bubbles during the EoR
    All quantitative results on marked statistics and Fisher constraints are derived from these simulations.

pith-pipeline@v0.9.0 · 5799 in / 1275 out tokens · 65679 ms · 2026-05-20T00:13:19.569239+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

81 extracted references · 81 canonical work pages · 2 internal anchors

  1. [1]

    Komatsu, K.M

    E. Komatsu, K.M. Smith, J. Dunkley, C.L. Bennett, B. Gold, G. Hinshaw et al.,Seven-year wilkinson microwave anisotropy probe (wmap*) observations: Cosmological interpretation,The Astrophysical Journal Supplement Series192(2011) 18

    work page 2011

  2. [2]

    R. Adam, N. Aghanim, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini et al., Planckintermediate results: Xlvii.planckconstraints on reionization history,Astronomy and amp; Astrophysics596(2016) A108

    work page 2016

  3. [3]

    Aghanim, Y

    N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini et al., Planck2018 results: Vi. cosmological parameters,Astronomy and amp; Astrophysics641(2020) A6

    work page 2020

  4. [4]

    Becker, X

    R.H. Becker, X. Fan, R.L. White, M.A. Strauss, V.K. Narayanan, R.H. Lupton et al.,Evidence for reionization at z-6: Detection of a gunn-peterson trough in a z=6.28 quasar,The Astronomical Journal122(2001) 2850–2857

    work page 2001

  5. [5]

    Fan, M.A

    X. Fan, M.A. Strauss, D.P. Schneider, R.H. Becker, R.L. White, Z. Haiman et al.,A survey of z=5.7 quasars in the sloan digital sky survey. ii. discovery of three additional quasars at z=6, The Astronomical Journal125(2003) 1649–1659. – 27 –

    work page 2003

  6. [6]

    Barnett, S.J

    R. Barnett, S.J. Warren, G.D. Becker, D.J. Mortlock, P.C. Hewett, R.G. McMahon et al., Observations of the lyman series forest towards the redshift 7.1 quasar ulas j1120+0641, Astronomy and amp; Astrophysics601(2017) A16

    work page 2017

  7. [7]

    Ouchi, K

    M. Ouchi, K. Shimasaku, H. Furusawa, T. Saito, M. Yoshida, M. Akiyama et al.,Statistics of 207 ly alpha emitters at a redshift near 7: Constraints on reionization and galaxy formation models,The Astrophysical Journal723(2010) 869–894

    work page 2010

  8. [8]

    Zheng, J

    Z.-Y. Zheng, J. Wang, J. Rhoads, L. Infante, S. Malhotra, W. Hu et al.,First results from the lyman alpha galaxies in the epoch of reionization (lager) survey: Cosmological reionization at z-7,The Astrophysical Journal Letters842(2017) L22

    work page 2017

  9. [9]

    Taylor, L.L

    A.J. Taylor, L.L. Cowie, A.J. Barger, E.M. Hu and A. Songaila,The evolution of the ultraluminous ly alpha luminosity function over z = 5.7–6.6,The Astrophysical Journal914 (2021) 79

    work page 2021

  10. [10]

    Furlanetto, S

    S.R. Furlanetto, S. Peng Oh and F.H. Briggs,Cosmology at low frequencies: The 21cm transition and the high-redshift universe,Physics Reports433(2006) 181–301

    work page 2006

  11. [11]

    Pritchard and A

    J.R. Pritchard and A. Loeb,21 cm cosmology in the 21st century,Reports on Progress in Physics75(2012) 086901

    work page 2012

  12. [12]

    Paciga, J.G

    G. Paciga, J.G. Albert, K. Bandura, T.-C. Chang, Y. Gupta, C. Hirata et al.,A simulation-calibrated limit on the hi power spectrum from the gmrt epoch of reionization experiment,Monthly Notices of the Royal Astronomical Society433(2013) 639–647

    work page 2013

  13. [13]

    Abdurashidova, J.E

    Z. Abdurashidova, J.E. Aguirre, P. Alexander, Z.S. Ali, Y. Balfour, A.P. Beardsley et al.,First results from hera phase i: Upper limits on the epoch of reionization 21 cm power spectrum,The Astrophysical Journal925(2022) 221

    work page 2022

  14. [14]

    Mertens, M

    F.G. Mertens, M. Mevius, L.V.E. Koopmans, A.R. Offringa, S. Zaroubi, A. Acharya et al., Deeper multi-redshift upper limits on the epoch of reionisation 21-cm signal power spectrum from lofar between z=8.3 and z=10.1,Astronomy and amp; Astrophysics698(2025) A186

    work page 2025

  15. [15]

    Barry, M

    N. Barry, M. Wilensky, C.M. Trott, B. Pindor, A.P. Beardsley, B.J. Hazelton et al.,Improving the epoch of reionization power spectrum results from murchison widefield array season 1 observations,The Astrophysical Journal884(2019) 1

    work page 2019

  16. [16]

    Koopmans, J

    L. Koopmans, J. Pritchard, G. Mellema, J. Aguirre, K. Ahn, R. Barkana et al.,The cosmic dawn and epoch of reionisation with ska, inProceedings of Advancing Astrophysics with the Square Kilometre Array — PoS(AASKA14), AASKA14, Sissa Medialab, May, 2015, DOI

    work page 2015

  17. [17]

    Gehlot, F.G

    B.K. Gehlot, F.G. Mertens, L.V.E. Koopmans, M.A. Brentjens, S. Zaroubi, B. Ciardi et al., The first power spectrum limit on the 21-cm signal of neutral hydrogen during the cosmic dawn at z = 20–25 from lofar,Monthly Notices of the Royal Astronomical Society488(2019) 4271–4287

    work page 2019

  18. [18]

    Mertens, M

    F.G. Mertens, M. Mevius, L.V.E. Koopmans, A.R. Offringa, G. Mellema, S. Zaroubi et al., Improved upper limits on the 21cm signal power spectrum of neutral hydrogen at z = 9.1 from lofar,Monthly Notices of the Royal Astronomical Society493(2020) 1662–1685

    work page 2020

  19. [19]

    Abdurashidova, J.E

    Z. Abdurashidova, J.E. Aguirre, P. Alexander, Z.S. Ali, Y. Balfour, R. Barkana et al.,Hera phase i limits on the cosmic 21 cm signal: Constraints on astrophysics and cosmology during the epoch of reionization,The Astrophysical Journal924(2022) 51

    work page 2022

  20. [20]

    Acharya, F

    A. Acharya, F. Mertens, B. Ciardi, R. Ghara, L.V.E. Koopmans and S. Zaroubi,Revised lofar upper limits on the 21-cm signal power spectrum atz≈9.1using machine learning and gaussian process regression, 2024

    work page 2024

  21. [21]

    Ceccotti, A.R

    E. Ceccotti, A.R. Offringa, F.G. Mertens, L.V.E. Koopmans, S. Munshi, J.K. Chege et al., First upper limits on the 21-cm signal power spectrum of neutral hydrogen atz= 9.16from the lofar 3c196 field, 2025. – 28 –

    work page 2025

  22. [22]

    S.S. Gill, S. Bharadwaj, K.M.A. Elahi, S.K. Sethi and A.K. Patwa,The eor 21-cm bispectrum atz= 8.2from mwa data i: Foregrounds and preliminary upper limits, 2025

    work page 2025

  23. [23]

    Gill, K.M.A

    S.S. Gill, K.M.A. Elahi, S. Bharadwaj, S.K. Sethi and A.K. Patwa,The Epoch of Reionization 21 cm Bispectrum atz= 8.2from MWA data II: Smooth Component Filtering,2602.17304

    work page arXiv

  24. [24]

    Simpson, J.B

    F. Simpson, J.B. James, A.F. Heavens and C. Heymans,Clipping the cosmos: The bias and bispectrum of large scale structure,Physical Review Letters107(2011)

    work page 2011

  25. [25]

    Gruen, O

    D. Gruen, O. Friedrich, A. Amara, D. Bacon, C. Bonnett, W. Hartley et al.,Weak lensing by galaxy troughs in des science verification data, 2015

    work page 2015

  26. [26]

    Paillas, Y.-C

    E. Paillas, Y.-C. Cai, N. Padilla and A.G. S´ anchez,Redshift-space distortions with split densities,Monthly Notices of the Royal Astronomical Society505(2021) 5731–5752

    work page 2021

  27. [27]

    Paillas, C

    E. Paillas, C. Cuesta-Lazaro, W.J. Percival, S. Nadathur, Y.-C. Cai, S. Yuan et al., Cosmological constraints from density-split clustering in the boss cmass galaxy sample, 2023

    work page 2023

  28. [28]

    Banerjee and T

    A. Banerjee and T. Abel,Nearest neighbour distributions: New statistical measures for cosmological clustering,Monthly Notices of the Royal Astronomical Society500(2020) 5479–5499

    work page 2020

  29. [29]

    Cheng, Y.-S

    S. Cheng, Y.-S. Ting, B. M´ enard and J. Bruna,A new approach to observational cosmology using the scattering transform,Monthly Notices of the Royal Astronomical Society499(2020) 5902–5914

    work page 2020

  30. [30]

    Eickenberg, E

    M. Eickenberg, E. Allys, A.M. Dizgah, P. Lemos, E. Massara, M. Abidi et al.,Wavelet moments for cosmological parameter estimation, 2022

    work page 2022

  31. [31]

    Cheng, G.A

    S. Cheng, G.A. Marques, D. Grand´ on, L. Thiele, M. Shirasaki, B. M´ enard et al.,Cosmological constraints from weak lensing scattering transform using hsc y1 data,Journal of Cosmology and Astroparticle Physics2025(2025) 006

    work page 2025

  32. [32]

    Rubira and R

    H. Rubira and R. Voivodic,The effective field theory and perturbative analysis for log-density fields,Journal of Cosmology and Astroparticle Physics2021(2021) 070

    work page 2021

  33. [33]

    Krause, Y

    2pt Collaboration, E. Krause, Y. Kobayashi, A.N. Salcedo, M.M. Ivanov, T. Abel et al.,A parameter-masked mock data challenge for beyond-two-point galaxy clustering statistics, 2024

    work page 2024

  34. [34]

    Bharadwaj and S.K

    S. Bharadwaj and S.K. Pandey,Probing non-gaussian features in the h i distribution at the epoch of re-ionization,Monthly Notices of the Royal Astronomical Society358(2005) 968–976

    work page 2005

  35. [35]

    Iliev, G

    I.T. Iliev, G. Mellema, U.-L. Pen, H. Merz, P.R. Shapiro and M.A. Alvarez,Simulating cosmic reionization at large scales - i. the geometry of reionization: Simulating reionization at large scales,Monthly Notices of the Royal Astronomical Society369(2006) 1625–1638

    work page 2006

  36. [36]

    Mellema, I.T

    G. Mellema, I.T. Iliev, U.-L. Pen and P.R. Shapiro,Simulating cosmic reionization at large scales - ii. the 21-cm emission features and statistical signals,Monthly Notices of the Royal Astronomical Society372(2006) 679–692

    work page 2006

  37. [37]

    Majumdar, J.R

    S. Majumdar, J.R. Pritchard, R. Mondal, C.A. Watkinson, S. Bharadwaj and G. Mellema, Quantifying the non-gaussianity in the eor 21-cm signal through bispectrum,Monthly Notices of the Royal Astronomical Society476(2018) 4007–4024

    work page 2018

  38. [38]

    Majumdar, M

    S. Majumdar, M. Kamran, J.R. Pritchard, R. Mondal, A. Mazumdar, S. Bharadwaj et al., Redshifted 21-cm bispectrum – i. impact of the redshift space distortions on the signal from the epoch of reionization,Monthly Notices of the Royal Astronomical Society499(2020) 5090–5106

    work page 2020

  39. [39]

    Watkinson, B

    C.A. Watkinson, B. Greig and A. Mesinger,Epoch of reionization parameter estimation with the 21-cm bispectrum,Monthly Notices of the Royal Astronomical Society510(2022) 3838–3848. – 29 –

    work page 2022

  40. [40]

    Tiwari, A.K

    H. Tiwari, A.K. Shaw, S. Majumdar, M. Kamran and M. Choudhury,Improving constraints on the reionization parameters using 21-cm bispectrum,Journal of Cosmology and Astroparticle Physics2022(2022) 045

    work page 2022

  41. [41]

    Noble, M

    L. Noble, M. Kamran, S. Majumdar, C.S. Murmu, R. Ghara, G. Mellema et al.,Impact of the Epoch of Reionization sources on the 21-cm bispectrum,JCAP10(2024) 003 [2406.03118]

    work page arXiv 2024

  42. [42]

    Mahida, S.K

    Y. Mahida, S.K. Yadav, S. Majumdar, L. Noble, C.S. Murmu, S. Dasgupta et al.,From ANN to BNN: Inferring reionization parameters using uncertainty-aware emulators of 21-cm summaries,JCAP12(2025) 055 [2508.13261]

    work page arXiv 2025

  43. [43]

    Ebina and M

    H. Ebina and M. White,An analytically tractable marked power spectrum,Journal of Cosmology and Astroparticle Physics2025(2025) 150

    work page 2025

  44. [44]

    Stoyan,On correlations of marked point processes,Mathematische Nachrichten116(1984) 197 [https://onlinelibrary.wiley.com/doi/pdf/10.1002/mana.19841160115]

    D. Stoyan,On correlations of marked point processes,Mathematische Nachrichten116(1984) 197 [https://onlinelibrary.wiley.com/doi/pdf/10.1002/mana.19841160115]

    work page doi:10.1002/mana.19841160115 1984

  45. [45]

    Marked correlations in galaxy formation models

    R.K. Sheth, A.J. Connolly and R. Skibba,Marked correlations in galaxy formation models, astro-ph/0511773

    work page internal anchor Pith review Pith/arXiv arXiv

  46. [46]

    Beisbart and M

    C. Beisbart and M. Kerscher,Luminosity- and morphology-dependent clustering of galaxies, The Astrophysical Journal545(2000) 6

    work page 2000

  47. [47]

    Mark correlations: relating physical properties to spatial distributions

    C. Beisbart, M. Kerscher and K. Mecke,Mark correlations: relating physical properties to spatial distributions,physics/0201069

    work page internal anchor Pith review Pith/arXiv arXiv

  48. [48]

    Skibba, R.K

    R. Skibba, R.K. Sheth, A.J. Connolly and R. Scranton,The luminosity-weighted or ‘marked’ correlation function,Monthly Notices of the Royal Astronomical Society369(2006) 68 [https://academic.oup.com/mnras/article-pdf/369/1/68/18664730/mnras0369-0068.pdf]

    work page 2006

  49. [49]

    Skibba, K.L

    R.A. Skibba, K.L. Masters, R.C. Nichol, I. Zehavi, B. Hoyle, E.M. Edmondson et al.,Galaxy zoo: the environmental dependence of bars and bulges in disc galaxies: Environmental dependence of bars and bulges,Monthly Notices of the Royal Astronomical Society423(2012) 1485–1502

    work page 2012

  50. [50]

    Gottl¨ ober, M

    S. Gottl¨ ober, M. Kerscher, A.V. Kravtsov, A. Faltenbacher, A. Klypin and V. M¨ uller,Spatial distribution of galactic halos and their merger histories,Astronomy amp; Astrophysics387 (2002) 778–787

    work page 2002

  51. [51]

    Sheth,The halo-model description of marked statistics,Monthly Notices of the Royal Astronomical Society364(2005) 796–806

    R.K. Sheth,The halo-model description of marked statistics,Monthly Notices of the Royal Astronomical Society364(2005) 796–806

    work page 2005

  52. [52]

    White and N

    M. White and N. Padmanabhan,Breaking halo occupation degeneracies with marked statistics, Monthly Notices of the Royal Astronomical Society395(2009) 2381–2384

    work page 2009

  53. [53]

    G.-B. Zhao, B. Li and K. Koyama,Testing gravity using the environmental dependence of dark matter halos,Phys. Rev. Lett.107(2011) 071303

    work page 2011

  54. [54]

    Winther, D.F

    H.A. Winther, D.F. Mota and B. Li,Environment dependence of dark matter halos in symmetron modified gravity,The Astrophysical Journal756(2012) 166

    work page 2012

  55. [55]

    Lombriser, F

    L. Lombriser, F. Simpson and A. Mead,Unscreening modified gravity in the matter power spectrum,Phys. Rev. Lett.114(2015) 251101

    work page 2015

  56. [56]

    D. Shi, B. Li and J. Han,Environmental screening of dark matter haloes in f(r) gravity, Monthly Notices of the Royal Astronomical Society469(2017) 705 [https://academic.oup.com/mnras/article-pdf/469/1/705/49203330/mnras 469 1 705.pdf]

    work page 2017

  57. [57]

    Armijo, Y.-C

    J. Armijo, Y.-C. Cai, N. Padilla, B. Li and J.A. Peacock,Testing modified gravity using a marked correlation function,Monthly Notices of the Royal Astronomical Society478(2018) 3627 [https://academic.oup.com/mnras/article-pdf/478/3/3627/25072375/sty1335.pdf]. – 30 –

    work page 2018

  58. [58]

    Satpathy, R

    S. Satpathy, R. ACCroft, S. Ho and B. Li,Measurement of marked correlation functions in sdss-iii baryon oscillation spectroscopic survey using lowz galaxies in data release 12,Monthly Notices of the Royal Astronomical Society484(2019) 2148 [https://academic.oup.com/mnras/article-pdf/484/2/2148/27620577/stz009.pdf]

    work page 2019

  59. [59]

    Hern´ andez-Aguayo, J

    C. Hern´ andez-Aguayo, J. Hou, B. Li, C.M. Baugh and A.G. S´ anchez,Large-scale redshift space distortions in modified gravity theories,Monthly Notices of the Royal Astronomical Society485 (2019) 2194–2213

    work page 2019

  60. [60]

    Armijo, C.M

    J. Armijo, C.M. Baugh, P. Norberg and N.D. Padilla,A new test of gravity – i. introduction to the method,Monthly Notices of the Royal Astronomical Society529(2024) 2866–2876

    work page 2024

  61. [61]

    White,A marked correlation function for constraining modified gravity models,Journal of Cosmology and Astroparticle Physics2016(2016) 057–057

    M. White,A marked correlation function for constraining modified gravity models,Journal of Cosmology and Astroparticle Physics2016(2016) 057–057

    work page 2016

  62. [62]

    Aviles,Testing modified gravity theories with marked statistics,2110.13767

    A. Aviles,Testing modified gravity theories with marked statistics,2110.13767

    work page arXiv

  63. [63]

    Y. Yang, H. Miao, Q. Ma, M. Liu, C.G. Sabiu, J. Forero-Romero et al.,Using the mark weighted correlation functions to improve the constraints on cosmological parameters,The Astrophysical Journal900(2020) 6

    work page 2020

  64. [64]

    Marinucci, G

    M. Marinucci, G. Jung, M. Liguori, A. Ravenni, F. Spezzati, A. Andrews et al.,The constraining power of the marked power spectrum: an analytical study,2411.14377

    work page arXiv

  65. [65]

    Massara, F

    E. Massara, F. Villaescusa-Navarro, S. Ho, N. Dalal and D.N. Spergel,Using the marked power spectrum to detect the signature of neutrinos in large-scale structure,Phys. Rev. Lett.126 (2021) 011301

    work page 2021

  66. [66]

    Massara, F

    E. Massara, F. Villaescusa-Navarro, C. Hahn, M.M. Abidi, M. Eickenberg, S. Ho et al., Cosmological information in the marked power spectrum of the galaxy field,The Astrophysical Journal951(2023) 70

    work page 2023

  67. [67]

    Massara, C

    E. Massara, C. Hahn, M. Eickenberg, S. Ho, J. Hou, P. Lemos et al.,SimBIG: Cosmological constraints using simulation-based inference of galaxy clustering with marked power spectra, 2024

    work page 2024

  68. [68]

    Kamran, M

    M. Kamran, M. Sahl´ en, D. Sarkar and S. Majumdar,The re-markable 21-cm power spectrum i: Probing the hi distribution in the post-reionization era using marked statistics, 2024

    work page 2024

  69. [69]

    Cowell, J

    J.A. Cowell, J. Armijo, L. Thiele, G.A. Marques, C.P. Novaes, D. Grand´ on et al.,First constraints from marked angular power spectra with subaru hyper suprime-cam survey first-year data, 2025

    work page 2025

  70. [70]

    Ebina, M

    H. Ebina, M. White and E. Chaussidon,The marked power spectrum as a practical bispectrum measure for galaxy redshift surveys,2603.03581

    work page arXiv

  71. [71]

    Neyrinck, I

    M.C. Neyrinck, I. Szapudi and A.S. Szalay,Rejuvenating the matter power spectrum: Restoring information with a logarithmic density mapping,The Astrophysical Journal698(2009) L90–L93

    work page 2009

  72. [72]

    Neyrinck, I

    M.C. Neyrinck, I. Szapudi and A.S. Szalay,Rejuvenating power spectra. ii. the gaussianized galaxy density field,The Astrophysical Journal731(2011) 116

    work page 2011

  73. [73]

    Lombriser, F

    L. Lombriser, F. Simpson and A. Mead,Unscreening modified gravity in the matter power spectrum,Physical Review Letters114(2015)

    work page 2015

  74. [74]

    Choudhury, M.G

    T.R. Choudhury, M.G. Haehnelt and J. Regan,Inside-out or outside-in: the topology of reionization in the photon-starved regime suggested by ly alpha forest data,Monthly Notices of the Royal Astronomical Society394(2009) 960–977

    work page 2009

  75. [75]

    Majumdar, G

    S. Majumdar, G. Mellema, K.K. Datta, H. Jensen, T.R. Choudhury, S. Bharadwaj et al.,On the use of seminumerical simulations in predicting the 21-cm signal from the epoch of reionization,Monthly Notices of the Royal Astronomical Society443(2014) 2843–2861. – 31 –

    work page 2014

  76. [76]

    Mondal, S

    R. Mondal, S. Bharadwaj and S. Majumdar,Statistics of the epoch of reionization (eor) 21-cm signal – ii. the evolution of the power-spectrum error-covariance,Monthly Notices of the Royal Astronomical Society464(2016) 2992–3004

    work page 2016

  77. [77]

    Furlanetto, M

    S.R. Furlanetto, M. Zaldarriaga and L. Hernquist,The growth of h ii regions during reionization,The Astrophysical Journal613(2004) 1–15

    work page 2004

  78. [78]

    McKinley, G

    B. McKinley, G. Bernardi, C.M. Trott, J.L.B. Line, R.B. Wayth, A.R. Offringa et al., Measuring the global 21-cm signal with the mwa-i: improved measurements of the galactic synchrotron background using lunar occultation,Monthly Notices of the Royal Astronomical Society481(2018) 5034–5045

    work page 2018

  79. [79]

    Cowell, D

    J.A. Cowell, D. Alonso and J. Liu,Optimizing marked power spectra for cosmology,Monthly Notices of the Royal Astronomical Society535(2024) 3129–3140

    work page 2024

  80. [80]

    Mondal, S

    R. Mondal, S. Bharadwaj, S. Majumdar, A. Bera and A. Acharyya,The effect of non-gaussianity on error predictions for the epoch of reionization (eor) 21-cm power spectrum, Monthly Notices of the Royal Astronomical Society: Letters449(2015) L41–L45

    work page 2015

Showing first 80 references.