Forecasts of cosmological constraints from HI intensity mapping with FAST, BINGO & SKA-I

Elimboto Yohana; Yi-Chao Li; Yin-Zhe Ma

REVIEW 3 major objections 3 minor 73 references

Forecasts of cosmological constraints from HI intensity mapping with FAST, BINGO & SKA-I

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

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Pith's one-line read The paper forecasts that SKA-I single-dish HI intensity mapping gives the tightest dark-energy constraints among BINGO, FAST, and SKA-I, with one-year 1σ errors (w0, wa) = (0.3158, 0.4622).

desk verdict The IM-only ranking (SKA-I > FAST > BINGO) is probably right; the Planck-combined numbers are over-tight because two parameters were dropped instead of marginalized. read the letter →

arxiv 1908.03024 v1 pith:WAC5IBFH submitted 2019-08-08 astro-ph.CO

Elimboto Yohana , Yi-Chao Li , Yin-Zhe Ma This is my paper · ORCID

classification astro-ph.CO

keywords HIintensitymapping21cmcosmologyFishermatrixforecastdarkenergyequationofstateBINGOtelescopeFASTSKA-Itomographicangularpowerspectrum

topics Dark Energy

open problems Dark Energy

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 forecasts what three radio telescopes—BINGO, FAST, and SKA-I in single-dish mode—would learn about cosmology from one year of neutral-hydrogen (HI) intensity-mapping observations. Its central result is a ranking: SKA-I would give the tightest dark-energy equation-of-state constraints, with marginalized $1\sigma$ errors $(w_0, w_a) = (0.3158, 0.4622)$, followed by FAST and then BINGO; relative to BINGO these are improvements of 66.02% on $w_0$ and 87.09% on $w_a$. Adding Planck data tightens SKA-I to $(0.0678, 0.2679)$, a 37.22% and 30.33% improvement over Planck alone. The forecast also finds a parameter-by-parameter trade-off: FAST wins on small-scale-sensitive parameters such as $n_s$, $\Omega_c h^2$, $H_0$, and $\ln(10^{10}A_s)$, while SKA-I wins on $w_0$, $w_a$, $\Omega_\nu h^2$, and $N_{\rm eff}$. The authors intend these numbers as a benchmark for the relative capabilities of the next-generation HI intensity-mapping surveys.

What carries the argument

The load-bearing object is the tomographic HI angular power spectrum $C_\ell^{ij}$ of Eq. (3.1), computed from a transfer function that includes redshift-space distortions and is multiplied by a Gaussian beam window. It is compared with the single-dish thermal noise power spectrum $N_\ell^{ij} = \delta^{ij} T_{\rm sys}^2 S_{\rm survey}/(N_{\rm ant} N_{\rm feed} t_{\rm TOT}\Delta\nu)$ via the Fisher matrix $F_{\alpha\beta} = f_{\rm sky}\sum_\ell (2\ell+1)/2\,\mathrm{tr}[C_{\ell,\alpha}\Sigma_\ell C_{\ell,\beta}\Sigma_\ell]$ with $\Sigma_\ell=(C_\ell+N_\ell)^{-1}$ and diagonal noise. This converts telescope specifications (dish diameter, receiver temperature, frequency range, survey area, channel width) into predicted marginalized $1\sigma$ errors for nine cosmological parameters, and lets the paper rank the three experiments and their Planck combinations.

What would settle it

Measure the off-diagonal foreground-residual noise matrix in the first year of real single-dish HI data: if $N_\ell$ has significant correlations between frequency channels at $\ell<10$, the headline SKA-I errors $(0.3158, 0.4622)$ move toward the paper's own $\ell\geq10$ values $(0.4059, 0.5735)$, and the forecast is optimistic. A second check is to measure $\Omega_{\rm HI} b_{\rm HI}$ directly from the cross-correlation of an HI intensity map with an optical galaxy survey; a value different from the fiducial $0.62\times10^{-3}$ rescales the signal amplitude in Eq. (3.2) and with it all the quoted constraints.

Watch

Extended reading notes

Core claim

The paper claims that SKA-I, used as an array of single dishes in autocorrelation mode, will impose the most stringent dark-energy equation-of-state constraints of the three HI intensity-mapping experiments considered, reaching marginalized $1\sigma$ errors $(w_0, w_a) = (0.3158, 0.4622)$ after one year of observation. FAST improves on BINGO by 56.04% on $w_0$ and 55.64% on $w_a$, and SKA-I improves on BINGO by 66.02% and 87.09%. When each experiment's Fisher matrix is added to Planck's, SKA-I + Planck gives $(0.0678, 0.2679)$, which is 18.51% and 23.89% tighter than BINGO + Planck and 37.22% and 30.33% tighter than Planck alone. The paper further claims that across the nine cosmological parameters no single experiment dominates: FAST's larger dish gives it the edge on small angular scales ($n_s$, $\Omega_c h^2$, $H_0$, $\ln(10^{10}A_s)$), while SKA-I's wider frequency coverage (350–1050 MHz) gives it the edge on $w_0$, $w_a$, $\Omega_\nu h^2$, and $N_{\rm eff}$.

Load-bearing premise

Every quoted error bar assumes foregrounds are cleaned perfectly so that the noise between different frequency channels is uncorrelated and diagonal, and it further assumes a fixed HI signal amplitude even though the clustering bias multiplying that amplitude is never specified in the paper.

Editorial extensions

If this is right

SKA-I single-dish HI intensity mapping, run for one year, is predicted to give marginalized $1\sigma$ errors $(w_0, w_a) = (0.3158, 0.4622)$, about 66% tighter on $w_0$ and 87% tighter on $w_a$ than BINGO.
Combining SKA-I with Planck tightens these to $(0.0678, 0.2679)$, a 37.22% improvement over Planck alone on $w_0$ and 30.33% on $w_a$.
FAST is predicted to lead on small-scale-sensitive parameters ($n_s$, $\Omega_c h^2$, $H_0$, $\ln(10^{10}A_s)$), while SKA-I leads on $w_0$, $w_a$, $\Omega_\nu h^2$, and $N_{\rm eff}$; neither survey dominates the full parameter set.
Using 1 MHz rather than 10 MHz frequency channels substantially improves constraints by preserving redshift-space-distortion information along the line of sight.
Removing the foreground-contaminated modes $\ell<10$ inflates SKA-I's $w_0$ error from 0.3158 to 0.4059, so the quality of foreground cleaning directly controls whether the headline precision is reached.

Reading between the lines

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

The paper's own $\ell\geq10$ table suggests the headline $(w_0, w_a)$ errors are best-case numbers: if foreground residuals survive at $\ell<10$, SKA-I's $w_0$ error grows from 0.3158 to 0.4059, so the 66% and 87% improvements over BINGO should be read as contingent on clean large-scale modes.
Because the signal amplitude entering Eq. (3.2) is set by $\Omega_{\rm HI}$ and an unspecified HI clustering bias, a direct measurement of $\Omega_{\rm HI} b_{\rm HI}$ from HI-galaxy cross-correlation would convert these relative rankings into calibrated absolute predictions.
A natural next step, not taken here, is to combine FAST and SKA-I Fisher matrices: their complementary strengths (small angular scales versus wide frequency range) suggest joint constraints could beat either experiment alone, especially on $w_a$ and $n_s$.
The 1 MHz channelization test points to a computational and modelling cost: real receivers will have correlated noise across adjacent narrow channels, so the diagonal-noise approximation that carries this forecast will need to be relaxed in the analysis pipeline.

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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

Short version: the paper's main qualitative answer—SKA-I single-dish beats FAST, which beats BINGO, for w0–wa—survives contact with the text and with the ℓ≥10 test. The Planck-combined numbers, however, are not what they are labeled. The stress-test note is right: the authors add the Planck Fisher matrix 'entry-wise' for seven parameters and simply omit Neff and Σmν. In a 9×9 Fisher forecast, dropping a row/column is a delta-function prior, not a marginalization. The correct move is to embed the Planck prior in the 9×9 problem (zero blocks for the omitted parameters, or the full Planck covariance), invert, then marginalize. As written, the SKA-I+Planck (w0, wa) = (0.0678, 0.2679) and the 'improvement relative to Planck alone' percentages mix conditional quantities with the marginalized IM-only numbers. The combined claims in the abstract and Section 4 need to be redone or relabeled.

What is genuinely useful here is the updated, like-for-like comparison: 133-dish SKA-I specs, FAST at 10,000 deg2 and 300-m aperture, BINGO at 3,000 deg2; 10 MHz and 1 MHz channelization; and the ℓ≥10 robustness check. That last test matters because large-scale foreground cleaning is the usual Achilles' heel for IM forecasts; discarding ℓ<10 weakens constraints but does not change the ranking. The FAST/SKA-I trade-off—FAST better on ns and small-scale parameters, SKA-I better on wa and Ωνh2—is physically sensible and is the kind of result survey planning can use. The authors are also honest about the diagonal-noise, perfect-foreground assumption.

Soft spots, in proportion. The unstated HI bias is a real gap: Eq. (3.4) uses δn but the paper never says what b_HI is, and the absolute Fisher errors scale with the signal amplitude. This is less serious for the relative ranking, which is the paper's main claim. Foreground residuals and 1/f noise are deferred, which is fine for a forecast but should be labeled as optimistic. No code is provided; for a Fisher forecast with standard formulas that is an inconvenience, not a sin. The self-citation to Li & Ma and Xu, Ma & Weltman is fine.

Bottom line: this is a competent planning-level forecast with one load-bearing methodological mistake in the Planck-combined section. Send it to a serious referee; require them to fix the 7×7/9×9 combination and restate the combined errors as properly marginalized (or clearly labeled conditional). The IM-only comparison is worth keeping.

Referee Report

3 major / 3 minor

Summary. This paper presents Fisher-matrix forecasts of cosmological parameter constraints from single-dish HI intensity mapping with FAST, BINGO, and SKA-I. The signal is modeled through a tomographic angular power spectrum (Eqs. 3.1-3.4), the noise is treated as a diagonal thermal-noise covariance (Eq. 3.5), and a 9-parameter cosmological model is considered. The main quantitative claims are the marginalized 1σ errors (w0,wa) = (0.9293,3.5792), (0.4083,1.5878), and (0.3158,0.4622) for BINGO, FAST, and SKA-I, respectively, implying that SKA-I gives the strongest dark-energy constraints; combining with Planck tightens these to (0.0832,0.3520), (0.0791,0.3313), and (0.0678,0.2679). The paper also reports a trade-off between SKA-I and FAST across the other cosmological parameters and tests the robustness of the dark-energy results to discarding large angular scales (ℓ<10).

Significance. If the numbers are correct, the paper provides a useful, up-to-date comparison of three representative single-dish HI intensity mapping experiments and a transparent Fisher-matrix methodology that can be adapted to other surveys. Its strengths are the explicit signal and noise formulas, the use of narrow frequency channelizations, the comparison of old and updated SKA-I dish numbers, and the ℓ≥10 robustness test. The relative ranking of the three experiments for the dark-energy equation of state is plausible and likely robust to the issues discussed below. However, the absolute error forecasts rest on idealized assumptions (perfect foreground cleaning, diagonal noise, and an unspecified HI bias), and the Planck combination is not marginalized consistently. The absolute numbers and the quoted improvement percentages relative to Planck alone are therefore not all established as stated.

major comments (3)

[Section 3.3, Table 3] The Planck combination as implemented is not a marginalization over the full 9-parameter space. The text states that the Planck Fisher matrix is added 'entry-wise' for Ωb h², Ωc h², w0, wa, ln(10¹⁰As), H0, and ns, while Neff and Σmν/94.07 eV are omitted. Deleting rows and columns of a Fisher matrix before inversion is equivalent to fixing those parameters at their fiducial values, not to marginalizing over them. The IM-only columns in Table 3 are marginalized errors from the 9×9 Fisher matrix, whereas the combined columns are conditional errors from a 7×7 matrix. The correct procedure is to add the 9×9 Planck Fisher matrix (with zero blocks for the two parameters on which Planck has no information) to the 9×9 IM Fisher matrix, invert the full sum, and then extract the 7×7 marginal covariance. Until this is done, the quoted combined errors and the improvement percentages relative to Planck alone mix marginalized and conditional quantities, and the headline combined numbers in the Abstract and in Figures 3, 11, and 13 should be regarded as preliminary.
[Section 3.1, Eq. (3.4)] The signal amplitude in the forecast depends on the HI density contrast δn, but the HI clustering bias b_HI is never specified. In intensity mapping the HI density contrast is normally written δn = b_HI δm, and without a value (or a redshift-dependent model) for b_HI the amplitude of Cℓ, and therefore the absolute 1σ errors in Tables 3 and 4, is not uniquely determined. Ω_HI is fixed to 0.62×10⁻³, but b_HI is a separate and equally important multiplier. If the authors implicitly set b_HI = 1, this should be stated and justified. This issue does not necessarily change the relative ranking, but it prevents the quoted absolute error bars from being reproduced.
[Section 4.2 and Eq. (3.12)] The forecast assumes that foreground emission is cleaned perfectly and that the noise covariance is diagonal. Because the dark-energy information in this analysis comes substantially from large angular scales (ℓ≥2) and foreground residuals are expected to be largest there, the absolute constraints are optimistic. The ℓ≥10 test in Table 4 is a useful sensitivity check and shows that the ranking is stable, but it also shows a non-negligible loss of constraining power: for SKA-I alone, σ(w0) degrades from 0.3158 to 0.4059 and σ(wa) from 0.4622 to 0.5735. The headline numbers still include ℓ=2 and should be presented with a clear caveat that they are idealized upper limits under perfect foreground removal.

minor comments (3)

[Section 2.3 vs Section 4.1] The dish count for SKA-I is inconsistent: Table 2 and Section 2.3 use Nant = 133, while the text near Figure 8 and the final paragraph of Section 4.1 state that 'in this forecast we assume that the SKA-I project is an integrated 190 15-metre single-dishes in autocorrelated mode.' Please clarify which configuration was used for the Table 2 forecasts and, if necessary, recompute the affected numbers.
[Abstract vs Section 4.1] The FAST improvement over BINGO for w0 is quoted as 56.04% in the Abstract and 56.06% in Section 4.1; the latter follows from the stated numbers, so the Abstract should be corrected.
[Table 3 caption] The caption describes the columns as 'covariance matrices' but the entries are 1σ errors; please use consistent terminology such as '1σ marginalized errors'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the forecasts are self-contained Fisher-matrix calculations from stated signal, noise, and Planck inputs; the self-citations are not load-bearing.

full rationale

The central quantitative claims (BINGO/FAST/SKA-I 1-sigma errors and Planck-combined errors) are obtained by evaluating Eq. (3.11), F_alpha_beta = f_sky sum_ell ((2ell+1)/2) tr[C_ell,alpha Sigma_ell C_ell,beta Sigma_ell], with Sigma_ell = (C_ell + N_ell)^-1, using the tomographic angular spectra of Eq. (3.1) and the stated noise model of Eq. (3.5). No parameter is fitted to the forecasted constraints; Table 1 supplies external Planck fiducial values and Table 2 supplies experimental specifications. The Planck Fisher matrix is an external input computed from Planck Legacy Archive chains, and its entry-wise addition is a stated combination rule. Overlapping-author citations (Li & Ma 2017 for the diagonal noise treatment; Xu, Ma & Weltman 2018 for narrow-band redshift-space-distortion effects; Bigot-Sazy et al. 2016 for the FAST/BINGO ranking) are used as references or supporting context, not as the source of the forecasted ranking; the ranking is reproduced by the paper's own Fisher-matrix calculation. A statistical concern exists: Section 3.3 says Neff and Sigma m_nu/94.07 eV were 'omitted' when adding Planck, and Table 3 shows dashes for these parameters in combined columns; if the 7x7 sub-block is inverted directly, the combined errors are conditional rather than marginalized, which would make the quoted Planck gains over-tight. This is a modeling/statistical point, not circularity: the quoted numbers are not equal by construction to any fitted input, and no fitted parameter is renamed as a prediction. Therefore no circular step is identified.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

Everything that drives the forecast numbers is in the assumed signal and noise model. The main external input is Ω_HI from Switzer et al. (2013); the HI bias is never quoted. The experimental choices (survey area, receiver temperature, integration time, channel width) are taken from design documents and hand-picked values in Table 2. The Fisher formalism is standard. No new physical entities are introduced.

free parameters (3)

Ω_HI (fractional HI density) = 0.62e-3
Assumed from Switzer et al. (2013) in Eq. (3.2); the HI brightness temperature and hence the signal power scale with Ω_HI, so the forecasted 1σ errors depend on this value.
HI bias b_HI = unstated (implicitly 1)
No bias model is given for the HI overdensity in Eq. (3.4); the clustering signal amplitude scales as (b_HI Ω_HI)^2, making the absolute forecasts depend on an unspecified parameter.
Survey area S_survey = FAST 10,000 deg², SKA-I 10,000 deg², BINGO 3,000 deg²
Hand-picked in Table 2 and justified in Section 4.1 as 'moderate'; the differing sky coverage directly affects the noise level (Eq. 3.5) and therefore the headline improvement of FAST/SKA relative to BINGO.

assumptions (4)

standard math The likelihood of the observed angular power spectrum is Gaussian, so the Fisher matrix (Eq. 3.11) yields the parameter covariance.
Invoked in Section 3.3 without proof; standard MLE asymptotics for large-scale structure forecasts.
domain assumption Foregrounds are cleaned perfectly, leaving only independent thermal noise between frequency channels.
Assumed in Sections 3.2-3.3; the authors explicitly defer realistic foregrounds and 1/f noise to future work (Section 4.2).
domain assumption The HI density contrast in Eq. (3.4) is a valid model of the clustering signal, with an unspecified bias.
The temperature fluctuation transfer function is taken from Hall et al. 2013a, but the HI bias is never set, so the signal normalization is incomplete.
ad hoc to paper The IM Fisher matrices can be combined with Planck by entry-wise addition on the 7 overlapping parameters, omitting N_eff and m_ν.
Section 3.3: N_eff and Σm_ν are dropped in the combined runs to match the Planck chains, which changes the parameter space relative to the IM-only 9-parameter runs.

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Cite this review

Pith. "Pith review of Forecasts of cosmological constraints from HI intensity mapping with FAST, BINGO & SKA-I." pith.science (2026). https://pith.science/paper/WAC5IBFH

@misc{pith2026190803024,
  author       = {Pith},
  title        = {Pith review of: Forecasts of cosmological constraints from HI intensity mapping with FAST, BINGO & SKA-I},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WAC5IBFH}},
  note         = {Machine review of arXiv:1908.03024}
}

abstract

We forecast the cosmological constraints of the neutral hydrogen (HI) intensity mapping (IM) technique with radio telescopes by assuming 1-year of observational time. The current and future radio telescopes we consider here are FAST (Five hundred meter Aperture Spherical Telescope), BINGO (Baryon acoustic oscillations In Neutral Gas Observations), and SKA-I (Square Kilometre Array phase I) single-dish experiment. We also forecast the combined constraints of the three radio telescopes with Planck. We find that, the $1 \sigma$ errors of $(w_{0}, w_{a})$ for BINGO, FAST and SKA-I with respect to the fiducial values are respectively, $(0.9293, 3.5792), (0.4083, 1.5878), (0.3158, 0.4622)$. This is equivalent to $(56.04\%, 55.64\%)$ and $(66.02\%, 87.09\%)$ improvements in constraining $(w_{0}, w_{a})$ for FAST and SKA-I relative to BINGO. Simulations further show that SKA-I will put more stringent constraints than both FAST and BINGO when each of the experiment is combined with Planck measurement. For the $9$ cosmological parameters in consideration, we find that, there is a trade-off between SKA-I and FAST in constraining cosmological parameters, with each experiment being more superior in constraining a particular set of parameters.

Figures

Figures reproduced from arXiv: 1908.03024 by the authors.

**Figure 1.** The noise power spectra Nℓ (dashed line) and beam convolved angular power spectra, Cℓ (solid line) for FAST (red), BINGO (black) and SKA-I (green) at approximately overlapped frequencies. As expected, we see that the angular power spectra have almost the same profile at large scales but deviating with increase in number of multipoles, ℓ. Beyond ℓ = 150, angular power spectra for BINGO and SKA-I more rapidly become i… view at source ↗

**Figure 2.** w0 versus wa, 1σ (solid line) and 2σ (dashed line) cosmological constraints for FAST (red), BINGO (black) and SKA-I (green). cross-correlation studies involving SDSS-like experiments, FAST and SKA-I. In addition, it is practical to choose this survey area for FAST and SKA-I comparisons because the marginal increase of FAST FoM is quite small if Ωsur > 10, 000, so we will use Ωsur = 10, 000 in our forecast. BINGO (Bi… view at source ↗

**Figure 3.** w0 versus wa, 1σ (solid line) and 2σ (dashed line) cosmological constraints for Planck (blue), FAST + Planck (red), BINGO + Planck (black) and SKA-I + Planck (green). 5 5 5 5 5 5 √ [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗

Figures from the paper (13 more)

**Figure 4.** Figure 4: Figure of merit (FoM): inverse square root of the dete [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]

**Figure 5.** Figure 5: w0 versus wa, 1σ (solid line) and 2σ (dashed line) cosmological constraints for SKA-I split into lower frequency band (purple), high frequency band (cyan) and full range (red) of SKA-I frequencies. 5 5 5 5 5 5 √ …

**Figure 6.** Figure 6: Figure of merit (FoM): inverse square root of the dete [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]

**Figure 7.** Figure 7: SKA-I variation of system temperature, Tsys against frequency, ν. −1.8 −1.6 −1.4 −1.2 −1.0 −0.8 −0.6 −0.4 −0.2 w0 −1.0 −0.5 0.0 0.5 1.0 wa SKA-I: 190 dishes SKA-I: 133 dishes [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]

**Figure 8.** Figure 8: 1σ (solid line) and 2σ (dashed line) comparisons of SKA-I (SKAI-MID Band I) constraints on the dark energy EoS by considering early proposition of 190 number of dishes (red), and the updated (green) 133 number of dishes. the former number of dishes is to illustrate how…

**Figure 9.** Figure 9: Forecasts of cosmological constraints with FAST, BI [PITH_FULL_IMAGE:figures/full_fig_p019_9.png]

**Figure 10.** Figure 10: The relative percentage improvement for FAST and SK [PITH_FULL_IMAGE:figures/full_fig_p020_10.png]

**Figure 11.** Figure 11: Forecasts of joint cosmological constraints with e [PITH_FULL_IMAGE:figures/full_fig_p021_11.png]

**Figure 12.** Figure 12: The relative percentage improvement for FAST + [PITH_FULL_IMAGE:figures/full_fig_p022_12.png]

**Figure 13.** Figure 13: The relative percentage improvement for BINGO + [PITH_FULL_IMAGE:figures/full_fig_p022_13.png]

**Figure 14.** Figure 14: Forecasts of cosmological constraints with FAST, B [PITH_FULL_IMAGE:figures/full_fig_p023_14.png]

**Figure 15.** Figure 15: w0 versus wa, 1σ (solid line) and 2σ (dashed line) cosmological constraints for FAST (red), BINGO (black) and SKA-I (green) for minimum multipole moment, ℓ = 10. −1.2 −1.1 −1.0 −0.9 −0.8 w0 −1.00 −0.75 −0.50 −0.25 0.00 0.25 0.50 0.75 1.00 wa Planck BINGO + Planck FAST…

**Figure 16.** Figure 16: w0 versus wa, 1σ (solid line) and 2σ (dashed line) cosmological constraints for Planck (blue) FAST + Planck (red), BINGO + Planck (black) and SKA-I + Planck (green) for minimum multipole moment, ℓ = 10. parameters, not directly constraining some parameters by assuming…

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