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arxiv: 2606.30200 · v1 · pith:ONO56EVHnew · submitted 2026-06-29 · 🌌 astro-ph.CO

Cosmology with Intensity Mapping via Statistics Beyond the Power Spectrum in the SKAO Era

Suman Majumdar , Debanjan Sarkar , Leon Noble , Manas Mohit Dosibhatla , Zhaoting Chen , Bernhard Vos-Gin\'es , Vishrut Pandya , Mohd Kamran
show 33 more authors
Sourav Pal Chandra Shekhar Murmu Cora Uhlemann Pauline Gorbatchev Jean-Luc Starck Jos\'e Luis Bernal Marta Spinelli Caroline S. Heneka Matteo Viel Gabriella De Lucia Fabio Fontanot Stefano Camera Steve Cunnington Benedetta Spina Dionysis Karagiannis Samit Kumar Pal Anshuman Tripathi Sarah Libanore Abinash Kumar Shaw Rajesh Mondal Yashrajsinh Mahida Yashar Akrami Philip Bull Chris Clarkson Abhirup Datta Jos\'e Fonseca Yin-Zhe Ma Roy Maartens Liantsoa F. Randrianjanahary Martin Sahlen Xin Wang Yougang Wang Jochen Weller
This is my paper

Pith reviewed 2026-06-30 05:13 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords 21-cm intensity mappinghigher-order statisticsSKAOnon-GaussianitybispectrumMinkowski functionalscosmology
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The pith

Future SKAO observations will measure higher-order 21-cm statistics to break parameter degeneracies.

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

The neutral hydrogen distribution in the post-reionization universe is non-Gaussian owing to nonlinear structure formation and galaxy biasing. Standard two-point statistics therefore miss part of the cosmological information contained in 21-cm intensity maps. This paper examines a suite of higher-order measures, from the bispectrum and probability density functions to morphological descriptors such as Minkowski functionals. It provides forecasts for their detection in upcoming SKAO surveys, taking into account instrumental noise, observational effects, and foreground removal. If the forecasts are accurate, these additional statistics will help separate astrophysical from cosmological signals and increase the overall constraining power of intensity mapping.

Core claim

The central claim is that several higher-order statistics applied to 21-cm intensity maps remain detectable with the sensitivity of the future Square Kilometre Array Observatory, even after realistic noise and foreground cleaning, thereby allowing tighter constraints on cosmological and astrophysical parameters.

What carries the argument

Higher-order statistics including the bispectrum, marked statistics, voxel intensity distributions, and Minkowski functionals applied to 21-cm intensity maps.

If this is right

  • These statistics will be measured more precisely than before.
  • Degeneracies between astrophysical and cosmological parameters can be reduced.
  • The total scientific return from SKAO intensity mapping surveys will increase.
  • Forecasts already include instrumental noise and foreground effects in some cases.

Where Pith is reading between the lines

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

  • Similar higher-order analyses could be applied to data from other radio telescopes.
  • Constraints on primordial non-Gaussianity might improve as a byproduct.
  • New computational methods will likely be required to compute these statistics on large maps.

Load-bearing premise

Higher-order statistics remain measurable and informative after realistic instrumental noise, observational effects, and foreground removal are included.

What would settle it

A detailed simulation in which the forecasted signal-to-noise ratios for the bispectrum or Minkowski functionals drop below detection thresholds once full noise and foreground models are applied.

Figures

Figures reproduced from arXiv: 2606.30200 by Abhirup Datta, Abinash Kumar Shaw, Anshuman Tripathi, Benedetta Spina, Bernhard Vos-Gin\'es, Caroline S. Heneka, Chandra Shekhar Murmu, Chris Clarkson, Cora Uhlemann, Debanjan Sarkar, Dionysis Karagiannis, Fabio Fontanot, Gabriella De Lucia, Jean-Luc Starck, Jochen Weller, Jos\'e Fonseca, Jos\'e Luis Bernal, Leon Noble, Liantsoa F. Randrianjanahary, Manas Mohit Dosibhatla, Marta Spinelli, Martin Sahlen, Matteo Viel, Mohd Kamran, Pauline Gorbatchev, Philip Bull, Rajesh Mondal, Roy Maartens, Samit Kumar Pal, Sarah Libanore, Sourav Pal, Stefano Camera, Steve Cunnington, Suman Majumdar, Vishrut Pandya, Xin Wang, Yashar Akrami, Yashrajsinh Mahida, Yin-Zhe Ma, Yougang Wang, Zhaoting Chen.

Figure 1
Figure 1. Figure 1: Illustration of the iterative coarse-graining scheme used for percolation analysis. The four panels show the same slice of a field without coarse-graining (first from left) and after 2, 4, and 6 iterations in order. On each iteration, the cells sharing a face with a bright cell are marked as bright. The fields are binary, with the dark cells marked by zeros and the bright cells by ones. 2.5.2 Local Dimensi… view at source ↗
Figure 2
Figure 2. Figure 2: Left: Normalized HI PDF including telescope beam and foreground removal systematics, cal￾culated for smoothing scales 𝑅 = 15.5, 24.8, 31.0 Mpc/ℎ. Dashed lines do not include thermal noise, and solid lines include thermal noise. 1 − 𝜎 errors are represented as shaded contours. Right: (Ω𝑀, 𝜎8) Fisher forecast for SKA-Mid HI IM survey considering 𝑧 ∼ 1.1 − 1.5 and 𝑓sky = 0.3. We show 1𝜎 and 2𝜎 contours of the… view at source ↗
Figure 3
Figure 3. Figure 3: The forecast for the emission line stacking using single dish HI intensity mapping with SKA-Mid at 𝑧 ∼ 1.1 − 1.5. The blue solid line shows the expected HI signal. The outer orange shaded region shows the expected 3𝜎 noise level, whereas the inner region shows the 1𝜎 noise level. lower 𝑧. Among the ℓ = 2 quadrupoles, 𝑄 0 2 is strongest for linear and stretched triangles (𝜇 → 1, 𝑡 ≲ 0.8) and becomes suppres… view at source ↗
Figure 4
Figure 4. Figure 4: Heatmaps of the reduced bispectrum multipoles of the HI density contrast in the (𝜇, 𝑡)-plane. The dimensionless reduced bispectrum multipoles are defined as 𝑄 𝑚 ℓ = 𝐵 𝑚 ℓ /𝐵 𝑟 HI, where 𝐵 𝑚 ℓ denotes the redshift￾space bispectrum multipoles including the FoG effect, and 𝐵 𝑟 HI represents the real-space HI bispectrum. The results are shown for 𝑘1 = 0.1 ℎMpc−1 at redshift 𝑧 = 2. The redshift-space bispectrum… view at source ↗
Figure 5
Figure 5. Figure 5: Right: 21-cm bispectrum for all unique 𝑘 − triangles for 𝑘1 = 0.61Mpc−1 at 𝑧 = 0.99. Left: The signal-to-ratio of 21-cm bispectrum for all unique 𝑘 − triangles for 300 hours of observation per pointing with SKA-Mid. 𝑧 = 2, the thermal-noise power is 𝑃𝑁 (𝑘, 𝜇) = 𝐴𝑒 𝑇 2 sys 𝑟 2 (𝑧) 𝑡𝑘 𝑑𝑟 𝑑𝜈 , (18) where 𝑡𝑘 is the effective integration time per mode. The bispectrum multipoles are then estimated as weighted su… view at source ↗
Figure 6
Figure 6. Figure 6: Signal-to-noise ratio (SNR) maps of the bispectrum multipoles up to (ℓ, 𝑚) = (4, 1) in the (𝜇, 𝑡)- plane. The SNR is computed for 𝑘1 = 0.1 ℎ Mpc−1 at redshift 𝑧 = 2. For the 𝐵 0 ℓ multipoles with ℓ = 0, 2, 4, the SNR for SKA-Mid peaks at 𝜇 → 1 and 0.6 ≤ 𝑡 ≤ 0.85. The 𝐵 1 2 and 𝐵 1 4 multipoles exhibit maximum SNR near the linear triangle configurations (i.e., 𝜇 → 1, 0.75 ≤ 𝑡 ≤ 0.95), while the 𝐵 2 2 multip… view at source ↗
Figure 7
Figure 7. Figure 7: The dimensionless power spectrum of the matter (left panel), the H i (middle panel), and the H i with density values 𝜌/𝜌 <¯ 3.0 (right panel). The distribution is smoothed for a fixed radius of 𝑅 = 280 kpc. The power spectra are demonstrated as a function of 𝑘-mode at five different redshifts in the range 𝑧 ∼ 1–5. The shaded regions in each panel represent ±1𝜎 spread around the mean value at 𝑧 = 3. is poss… view at source ↗
Figure 8
Figure 8. Figure 8: Comparing the signal strength, at different 𝑘-modes, against the corresponding noise levels using marked statistics designed to boost the signal strength at redshift 𝑧 = 1 with the standard signal power spectrum. Left panel: The dimensionless HI power spectrum and mark power spectrum of the signal fluctuation and noise. Right panel: The dimensionless HI power spectrum and marked field power spectrum of the… view at source ↗
Figure 9
Figure 9. Figure 9: Left: ℓ1-norm of the starlet coefficients as a function of the bin threshold for five decomposition scales of the HI intensity map. Right: Posterior distributions for Ωc and 10−9 𝐴s inferred with simulation￾based inference (SBI). The green contours and curves correspond to the power spectrum 𝐶ℓ , and the purple ones to the Starlet ℓ1-norm. Contours indicate the 68% and 95% confidence regions. The inference… view at source ↗
Figure 10
Figure 10. Figure 10: Left: Signal-to-noise ratios (SNR) of the 21-cm brightness temperature fluctuations at spatial resolution 𝛿𝑥 ≃ 1 Mpc in the overlapping redshift range where SKA-Mid and SKA Phase 2 can observe the 21-cm and CO(1-0) LIM signals, respectively. The noise estimates are made assuming Gaussian random thermal noise for 5000 hours per pointing of SKA-Mid observations. The black dashed line corresponds to 𝑧 = 1.41… view at source ↗
Figure 11
Figure 11. Figure 11: Distribution of local dimensions of classifiable cells out of 105 randomly sampled bright cells in the galaxy density (top) and 𝑇21cm (bottom) maps simulated with galaxy positions in redshift space. The 𝐷 values are binned into intervals of size 0.5. The different curves correspond to different length scales specified by the 𝑅min and 𝑅max values. The vertical 1𝜎 error bars denote standard deviation in 𝑃(𝐷… view at source ↗
read the original abstract

The cosmological distribution of neutral hydrogen (HI) during the post-reionization era is highly non-Gaussian due to the underlying non-linear structure formation, complex galaxy biasing, and potential primordial non-Gaussianity. One needs higher-order (beyond two-point) statistics to maximally extract the non-Gaussian information out of the 21-cm intensity maps. This chapter summarizes the potential of several higher-order statistics, including voxel intensity distribution, emission line stacking, probability density functions, $\ell_1$-norm, bispectrum, and various marked statistics. Additionally, image-based morphological descriptors, such as the Largest Cluster Statistic, local dimensions, and Minkowski functionals, etc., can potentially characterize the morphology and geometry of the cosmic web encoded in the 21-cm intensity maps. This chapter presents forecasts of the detectability of these higher-order statistics in the context of the future SKAO observations. These forecasts incorporate instrumental noise, observational effects, and, in some cases, foreground removal in their analyses. With its unprecedented sensitivity, the future SKAO 21-cm observations will enable us to measure these higher-order statistics more precisely, possibly helping to break degeneracies between astrophysical and cosmological parameters, and maximizing the science outcome from these surveys.

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

1 major / 0 minor

Summary. The paper reviews several higher-order (beyond power spectrum) statistics—including voxel intensity distribution, emission-line stacking, PDFs, ℓ1-norm, bispectrum, marked statistics, Largest Cluster Statistic, local dimensions, and Minkowski functionals—for extracting non-Gaussian information from post-reionization 21-cm intensity maps. It presents SKAO forecasts for their detectability that incorporate instrumental noise and observational effects, and in some cases foreground removal, concluding that SKAO’s sensitivity will enable precise measurements that can break degeneracies between astrophysical and cosmological parameters.

Significance. If the forecasts are robust, the work demonstrates that non-Gaussian statistics can substantially increase the scientific return from SKAO 21-cm surveys by accessing information inaccessible to two-point statistics alone, with potential to tighten constraints on both cosmology and HI astrophysics.

major comments (1)
  1. [Abstract] Abstract: The central claim that SKAO observations 'will enable us to measure these higher-order statistics more precisely' rests on forecasts that 'incorporate instrumental noise, observational effects, and, in some cases, foreground removal.' Because foregrounds are the dominant systematic in 21-cm intensity mapping, the manuscript must explicitly identify which statistics and which survey configurations include realistic foreground cleaning (and which do not) and demonstrate that detectability and degeneracy-breaking power survive when foreground removal is performed; without this, the headline claim is not uniformly supported.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their thorough review and constructive feedback. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that SKAO observations 'will enable us to measure these higher-order statistics more precisely' rests on forecasts that 'incorporate instrumental noise, observational effects, and, in some cases, foreground removal.' Because foregrounds are the dominant systematic in 21-cm intensity mapping, the manuscript must explicitly identify which statistics and which survey configurations include realistic foreground cleaning (and which do not) and demonstrate that detectability and degeneracy-breaking power survive when foreground removal is performed; without this, the headline claim is not uniformly supported.

    Authors: We agree that foreground removal is the dominant systematic and that the abstract should be more explicit to uniformly support the central claim. The body of the manuscript already specifies, for each statistic, whether realistic foreground cleaning is included in the forecasts (e.g., for the bispectrum and Minkowski functionals in the relevant sections) or noted as a limitation (e.g., for voxel intensity distribution). To address the referee's point directly, we will revise the abstract to explicitly list the statistics and survey configurations that incorporate foreground removal and add a short statement confirming that the reported detectability and degeneracy-breaking results remain valid after foreground cleaning where it is applied. revision: yes

Circularity Check

0 steps flagged

No circularity: forecasts drawn from external simulations without self-referential reduction

full rationale

The paper is a summary chapter presenting higher-order statistics and SKAO forecasts. The abstract states that forecasts 'incorporate instrumental noise, observational effects, and, in some cases, foreground removal in their analyses' and that SKAO 'will enable us to measure these higher-order statistics more precisely'. No equations, fitted parameters renamed as predictions, or self-citation chains are exhibited that reduce any claimed result to its own inputs by construction. The central claims rest on external simulation pipelines and prior independent works rather than internal redefinition, satisfying the self-contained benchmark.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; the forecasts presumably rely on standard cosmological simulation pipelines and foreground models not detailed here.

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discussion (0)

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Reference graph

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