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REVIEW 4 major objections 6 minor 59 references

Redshift drift effect through the observation of HI 21cm signal with SKA

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read SKA 0.001 Hz mode can clock cosmic drift at sub-mm/s precision over half a year.

desk verdict The SKA 0.5-year redshift-drift forecast is a nice question, but the error model is unverifiable and the paper's own numbers disagree by orders of magnitude. read the letter →

arxiv 2501.15117 v1 pith:DA3S6LE4 submitted 2025-01-25 astro-ph.CO

Jiangang Kang , Tong-Jie Zhang , Peng He , Ming Zhu This is my paper · ORCID
classification astro-ph.CO
keywords redshiftdriftSandage-LoebeffectHI21cmlineSquareKilometreArraydarkenergyconstraintscosmicaccelerationspectralresolutioncosmologicalparameterforecasting
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

Using a half-year observing campaign, this paper argues that the Square Kilometre Array (SKA) can resolve the Sandage-Loeb redshift drift—the tiny change in a source's redshift caused by cosmic expansion—through redshifted HI 21cm line emission and absorption. The argument turns on two ultra-high spectral resolutions, 0.001 Hz and 0.002 Hz, which the paper shows are the SKA configurations whose frequency resolution beats the ~1.28 mm/s velocity-drift accuracy limit across z=0 to z=1. With roughly a billion HI galaxies and about 1,800 Damped Lyman-alpha systems, the forecast reaches sub-mm/s per-half-year precision, enough to constrain H0 near 70 km/s/Mpc, Omega_m near 0.3, and the dark-energy equation of state near w=-1. If correct, this makes the SL effect a practical, model-independent probe of cosmic acceleration in the SKA era rather than a decades-distant prospect.

What carries the argument

The load-bearing object is the Sandage-Loeb velocity-drift relation, $\frac{dv}{dt} = \frac{c H_0}{1+z}\\left[1+z - \frac{H(z)}{H_0}\\right]$, together with the error-forecasting formula $\\Delta v_{\\rm obs} = \\sigma_n N^{-1/2}(1+z)^{\\lambda} \\Delta\\nu^{1/2}$ in cm/s, where $\\sigma_n$ is a normalization constant set to 1 to 5 cm/s, $N$ is the number of detected 21cm sources per redshift bin, and $\\lambda$ is 1.09 for 0.001 Hz or 1.52 for 0.002 Hz. The forecast works by comparing this predicted precision against the theoretical drift signal: at 0.001 and 0.002 Hz the velocity drift is 0.01 to 0.21 mm/s, exceeding the 1.28 mm/s detection limit, so the measurement is signal-dominated rather than noise-dominated. The other machinery is the source census: fitted dN/dz coefficients for HI galaxy counts and a DLA incidence function, which convert the chosen spectral resolution into the number statistics that drive the error formula.

What would settle it

Measure sigma_n directly from SKA1 or SKA2 commissioning spectra by comparing observed channel-to-channel velocity residuals against the $N^{{-1/2}}$(1+z)^$\lambda$ $Delta_nu^{{1/2}}$ scaling in Eq (9) at 0.001 and 0.002 Hz; if the fitted sigma_n falls outside 1 to 5 cm/s, the claimed sub-mm/s precision and the H0, Omega_m, w, w0, and wa constraints do not hold. An independent check is to re-derive sigma_n from receiver temperature, integration time, and bandpass stability without invoking the in-prep normalization.

Watch

Extended reading notes

Core claim

The central claim is that the SKA, observing redshifted HI 21cm emission from face-on galaxies and 21cm absorption from Damped Lyman-$\alpha$ systems over a 0.5-year interval, can detect the cosmological redshift drift at z around 1 with velocity uncertainties of 0.01 to 0.21 mm/s, provided the spectral resolution is set to 0.001 or 0.002 Hz. The paper derives the required frequency resolution from the Lambda-CDM (Planck 2018) prediction that the frequency shift stays below 0.1 Hz, then uses source-count statistics with roughly $10^{7}$ galaxies per redshift bin to forecast error bars. The resulting simulated data recover best-fit parameters H0 near 67 to 70 km/s/Mpc, Omega_m near 0.29 to 0.33, w near -0.95, w0 near -1.0, and wa near -0.1 across the Lambda-CDM, wCDM, and CPL models. The paper concludes that the SL effect observed through HI 21cm lines is a viable real-time cosmological probe of dark energy.

Load-bearing premise

All the quoted precision depends on the normalization constant sigma_n in the error formula, which the paper sets to 1 to 5 cm/s citing only unpublished work; if the real SKA noise statistics differ, every velocity error and every recovered cosmological parameter changes with it.

Editorial extensions

If this is right

  • At 0.001 Hz spectral resolution, the projected HI 21cm emission sample reaches about 1.36 billion galaxies by z=1, giving per-bin velocity uncertainties of 0.01 to 0.03 cm/s per half-year.
  • Only the 0.001 and 0.002 Hz configurations achieve the required precision across the full z=0 to 1 range; 0.005 Hz and 0.01 Hz do not, so the experiment's feasibility rests on SKA delivering those two spectral modes.
  • Emission-line forecasts constrain H0 to sub-1% precision with best fits near 70 km/s/Mpc and Omega_m near 0.3, and tighten w, w0, and wa relative to current SN Ia and BAO constraints.
  • DLA absorption-line data, though yielding about 1,800 systems and weaker constraints with H0 uncertainties above 2.8, still recover the fiducial parameters and independently support the same acceleration signal.
  • A 0.5-year observing window, not a decade-long campaign, suffices for the SL signal if the spectral resolution and source counts are as assumed.

Reading between the lines

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

  • Beyond the paper's claims: if the normalization constant sigma_n in the error formula comes out higher than 5 cm/s in SKA commissioning data, the claimed sub-mm/s precision and all quoted parameter constraints degrade roughly linearly; a useful early test is to measure sigma_n with a single bright calibrator before full surveys begin.
  • Beyond the paper's claims: combining the emission and absorption channels in a joint likelihood could break some of the H0-Omega_m degeneracy visible in the paper's separate contours, since the two channels have different redshift weightings.
  • Beyond the paper's claims: the 0.001 and 0.002 Hz criterion suggests a natural target-selection strategy, prioritizing face-on galaxies with S/N at least 100 and single Gaussian profiles while using DLA systems mainly as cross-checks rather than primary drift anchors.
  • Beyond the paper's claims: extending the baseline to 1 or 5 years would not only shrink the 1/sqrt(N) error but also change the redshift dependence of the drift signal, offering a consistency check on dark-energy models that a single 0.5-year snapshot cannot provide.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper argues that with the SKA's high spectral resolution modes (0.001 and 0.002 Hz), the Sandage-Loeb redshift drift can be measured from HI 21cm emission and absorption over a 0.5-year observing campaign, reaching sub-mm/s precision near z~1. The authors construct mock 'observed' drift velocities using an error formula (Eq. 9), fit them within ΛCDM, wCDM, and CPL models, and report tight constraints on H0, Ωm, w, w0, and wa. The central claim is that these SKA configurations can provide real-time cosmological measurements of cosmic acceleration.

Significance. If fully substantiated, the paper would be a valuable forecast for a highly challenging observable, extending earlier Sandage-Loeb analyses to the HI 21cm emission and absorption channels with SKA. The comparative treatment of emission galaxies versus DLA absorption systems and of three dark-energy parametrizations is a useful framework. The paper also makes a clear falsifiable prediction about the required spectral resolution (0.001-0.002 Hz) for a 0.5-year experiment. However, the central detectability claim rests on an unvalidated and internally inconsistent error model, and the parameter constraints are derived from mock data without an explicit forecast framing. As it stands, the numerical results do not support the claimed precision, and the paper needs substantial reanalysis before its conclusions can be accepted.

major comments (4)
  1. [Section 4, Eq. (9) and Fig. 5] The stated inputs to Eq. (9) do not reproduce the plotted uncertainties. For the 0.001 Hz case, using N=10^7 per 0.1 bin as stated after Eq. (9), λ=1.09, Δν=0.001 Hz, and (1+z)=1.5 at z≈0.5, one obtains Δv_obs ≈ (1-5) × 1.6×10^-5 cm/s, i.e., roughly 1.6×10^-5 to 8×10^-5 cm/s. Even taking the larger counts N~10^8 shown in Fig. 4 gives values near 10^-5 cm/s. Fig. 5 and the text report observed uncertainties of 0.01-0.03 cm/s, about three orders of magnitude larger. Because the χ² statistic in Eq. (6) is built directly from these σ_i, the confidence contours in Figs. 6-11 are not reproducible from the stated equations and inputs, and the claimed constraints are not internally supported.
  2. [Section 4, Eq. (9)] The normalization constant σ_n, which controls the overall scale of every error bar in the forecast, is cited solely to an unpublished work ('Kang 2024, in prep'). No derivation, fitting procedure, or independent calibration is provided, and the scaling (1+z)^λ Δν^{1/2} is asserted without a reference or derivation. Since the entire detectability claim—sub-mm/s precision in 0.5 years—depends on this constant, the paper does not currently offer a verifiable basis for its central result.
  3. [Section 4, Figs. 5-11] The 'SKA data' points are mock data generated from the fiducial ΛCDM model using Eq. (9), but the text repeatedly refers to them as 'observed', 'SKA data', and 'empirically determined'. Fitting these mock points with the same models that generated them (ΛCDM, wCDM, CPL) guarantees recovery of the input parameters, so the reported confidence intervals are a property of the assumed noise model rather than an independent measurement. The paper must explicitly identify the analysis as a forecast, specify exactly how the mock data were generated, and discuss the role of the priors in Table 2 in shaping the contours.
  4. [Abstract, Section 4, Tables 3-4] The headline numerical claims are internally contradictory. The abstract quotes drift rates of 0.01-0.21 mm/s and 0.031-0.17 mm/s; Section 4 and Fig. 5 quote signals of 0.05-0.15 cm/s with uncertainties of 0.01-0.03 cm/s; and the conclusion states uncertainties of 2-5 mm/s. These are not equivalent under unit conversion. In addition, Table 3 reports Ω_m = 0.311^{+0.304}_{-2.214} for ΛCDM, whose lower 1σ bound is unphysical, and Table 4 contains similarly malformed intervals. The numerical results as presented are therefore not internally consistent.
minor comments (6)
  1. [Eq. (5)] Eq. (5) as written, Δv = kh [1 + E(z)/(1+z)], is inconsistent with Eq. (2); substituting Eq. (2) into Δv = ˙v Δt gives kh [1+z - E(z)]/(1+z). If this is a typographical error, it should be corrected; if it is not, the sign/structure error changes the predicted signal.
  2. [Table 2 and affiliations] There are several typos: 'Proir' should be 'Prior' in Table 2; 'Burerau' in the affiliations should be 'Bureau'; and 'constrainted' in Section 4 should be 'constrained'.
  3. [References] The reference list contains duplicate entries for Alves et al. (2019), Kanekar et al. (2001), and Rawlings & Schilizzi (2011); these should be consolidated.
  4. [Section 2, Figs. 2-3] The notation S_z and S_v is used without precise definitions of units; Fig. 3's caption calls the velocity drift 'dimensionless' even though it is expressed in cm/s. Please clarify the definitions and units.
  5. [Section 3] The sentence about peculiar motion states it 'will be attenuated to 10^-14' without specifying the units or the quantity; please clarify what is 10^-14 (e.g., a velocity, a fractional shift, a redshift).
  6. [Fig. 4] The y-axis label 'N' should specify that the counts are per 0.1 redshift bin, since the text alternates between 'N' and 'N per 0.1 redshift interval'.

Circularity Check

2 steps flagged · score 6.0 of 10

Central forecast is circular: 'observed' SKA points are predicted data from the fitted models, and the error normalization rests on an unpublished self-citation.

  1. fitted input called prediction [Section 4, Eq. (6), Figs. 5–7; Fig. 6 caption]
    "The observed redshift and velocity drift data from SKA, with spectral resolutions of 0.001 Hz (top panel) and 0.002 Hz (bottom panel), derived from the HI 21cm emission of individual galaxies, are depicted with green cross error bars. ... The constraints on the H0 and Ωm parameter space within the 1σ and 2σ confidence intervals, derived from the predicted data utilizing the SKA’s spectral resolutions of 0.001 Hz (blue contours) and 0.002 Hz (green contours)."

    The paper contains no real observations: points labeled 'observed' in Fig. 5 are the same forecast points labeled 'predicted data' in Fig. 6. Since no actual SKA observations exist, these Δv_obs points must be synthetic realizations of the theoretical drift in Eq. (2) under the same ΛCDM/wCDM/CPL models that Eq. (6) then fits. Recovering H0≈70, Ωm≈0.3, w≈−1 is therefore a self-consistency recovery of the input fiducial cosmology, not an independent constraint; the claimed constraints are forced by construction. The abstract's 'It estimates H0 of about 70 km/s/Mpc' presents this fitted input as a prediction.

  2. self citation load bearing [Section 4, Eq. (9)]
    "The normalization constant σn ranges from 1 to 5 cm/s, varying with spectral resolution and redshift (Kang 2024, in prep), and decreases linearly in both contexts."

    All σ_i entering the χ2 likelihood in Eq. (6) are computed from Eq. (9), so the entire claimed sub-mm/s precision and all dark-energy contours depend on the chosen σ_n. The only support given for σ_n is '(Kang 2024, in prep)' — an unpublished self-citation from the same group. No derivation, independent calibration, or external data anchors the 1–5 cm/s range; the detectability forecast thus reduces at its linchpin to an unverified input from the authors' own prior work.

full rationale

The headline claim — SKA with 0.001/0.002 Hz resolution measuring redshift drift at sub-mm/s precision and constraining dark energy — is not self-contained against external benchmarks. The 'observed' points used in the χ2 fit are the paper's own 'predicted data' generated from the same ΛCDM/wCDM/CPL models being fitted, so the recovery of the fiducial parameter values is a consistency check rather than an empirical prediction. Independently, Eq. (9), which supplies every σ_i, is calibrated solely by an unpublished self-citation ('Kang 2024, in prep') for its normalization σ_n, leaving the error forecast unanchored. A numerical check of Eq. (9) with the paper's stated inputs also gives ~1e-5 cm/s rather than the plotted 0.01–0.03 cm/s; that inconsistency is a correctness problem that reinforces, but is not itself, the circularity. The target-selection and source-count modeling otherwise follow standard forecast practice, but the central parameter constraints and precision claim reduce to the model assumed to generate the mock data plus a self-cited noise normalization.

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

The central forecast depends on a chain of unverified inputs: an unpublished noise constant, assumed galaxy counts and DLA abundances, and mock data generated from the same model that is later fitted. These are not independent evidence for the claimed precision.

free parameters (5)
  • sigma_n normalization = 1 to 5 cm/s
    Sets the overall noise level in Eq (9); cited to unpublished 'Kang 2024, in prep'.
  • lambda per spectral resolution = 1.09 for 0.001 Hz, 1.52 for 0.002 Hz
    Shape factor in Eq (9), adopted from Kloeckner et al. 2015.
  • c1 through c5 galaxy distribution coefficients = Two sets for 0.001 and 0.002 Hz cases
    Fits to SKA source counts from Yahya et al. 2015, Table 4.
  • DLA redshift distribution parameters = 0.027 and 1.682 in n(z) = (0.027 +/- 0.007)(1+z)^(1.682 +/- 0.2)
    DLA number density fit from Kanekar and Briggs 2004.
  • Prior ranges for H0, Omega_m, w, w0, wa = H0 in [60,80], Omega_m in [0.1,0.6], w in [-3,3], w0 in [-3,3], wa in [-3,3]
    Uniform priors chosen by hand, not fitted, but they shape the reported constraints.
assumptions (5)
  • standard math FLRW metric and the standard redshift drift equation, Eq (1) and Eq (2), are valid.
    The paper builds its forecast on the established Sandage-Loeb formalism without re-deriving it.
  • domain assumption The SKA can achieve spectral resolutions of 0.001 Hz and 0.002 Hz with sufficient stability.
    Section 2 assumes these resolutions are available; this is critical because only these two resolutions are claimed to work.
  • domain assumption At least 10^7 face-on HI galaxies per 0.1 redshift bin with S/N greater than 100 are detectable.
    Section 4 uses N=10^7 per bin in Eq (9) and Figure 4; if the source counts are lower, the precision claim fails.
  • domain assumption The noise model Eq (9), taken from Kloeckner et al. 2015, correctly describes the velocity error with the unpublished sigma_n values.
    The central precision numbers all derive from this scaling relation, including the unpublished normalization constant.
  • ad hoc to paper Mock data generated from the fiducial Lambda-CDM model can stand in for real observations when deriving confidence intervals.
    The 'observed' data in Figures 5 and 9 are synthetic; the paper treats them as real measurements in the abstract and conclusions.

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Cite this review

Pith. "Pith review of Redshift drift effect through the observation of HI 21cm signal with SKA." pith.science (2026). https://pith.science/paper/DA3S6LE4

@misc{pith2026250115117,
  author       = {Pith},
  title        = {Pith review of: Redshift drift effect through the observation of HI 21cm signal with SKA},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DA3S6LE4}},
  note         = {Machine review of arXiv:2501.15117}
}
abstract

This study presents the findings of using the Square Kilometre Array (SKA) telescope to measure redshift drift via the HI 21cm signal, employing semi-annual observational interval within redshift around z $\sim$ 1 with main goal is to directly gauge the universe's expansion acceleration rate with millimeter-per-second (mm/s) precision. The SKA can detect over a billion HI 21cm emissions from individual galaxies to the redshift z $\sim$ 2 and thousands of absorption lines from Damped Lyman-alpha (DLA) systems against bright quasars to the redshift z $\sim$ 13, with the sensitivity limit of 100 mJy. By utilizing SKA's high spectral resolution settings (0.001, 0.002, 0.005, 0.01 Hz) to detect redshift drift, particularly focusing on the 0.001 and 0.002 Hz configuration, one aims to achieve the necessary mm/s in precision measurement by the 0.5-year observation period. The velocity drift rate, crucially determined by the two operational regimes within 0.01 to 0.21 mm/s and 0.031 to 0.17 mm/s, respectively, exceeds the theoretical accuracy limit of 1.28 mm/s. The analysis thoroughly restricts cosmological parameters related to dark energy using the Sandage-Loeb (SL) signal from the HI 21cm emission and absorption lines. It estimates $\rm H_0$ of about 70 km/s/Mpc, $\rm \Omega_m$ near 0.3, with w close to -1, $\rm w_0$ around -1, and $\rm w_a$ approaching -0.1. These results strongly endorse the SL effect as an effective method for confirming cosmic acceleration and exploring the dark sector in real-time cosmology with the SKA.

Figures

Figures reproduced from arXiv: 2501.15117 by the authors.

Figure 2
Figure 2. The variation of the dimensionless redshift drift with different cosmological models and redshifts is depicted, where the colored lines from bottom to top denote the spec￾tral resolution capabilities of the SKA (0.001, 0.002, 0.005, 0.01 Hz), and the shaded regions in various colors indicate the ranges of specific parameter variations. 0.0 0.5 1.0 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0 CDM h[0.6, 0.8] 0.0 0.5 1.0 wCDM h = … view at source ↗
Figure 3
Figure 3. The variation in dimensionless velocity drift as a function of specific models and redshift is illustrated by four distinct lines from bottom to top, corresponding to the spec￾tral resolution capabilities of the SKA (0.001, 0.002, 0.005, 0.01 Hz). The shaded regions in different colors represent the range of specific parameters variations. search(Alves et al. 2019; Martins et al. 2021). Sz = 1 H100 ∆z ∆t = h [1 + z … view at source ↗
Figure 4
Figure 4. The redshift distribution of the number of extra￾galactic HI 21cm emissions detected by SKA at a spectral resolution of 0.001Hz (left) and 0.002Hz (right). 0.00 0.05 0.10 0.15 0.20 CDM SKA data ( = 0.001Hz) CPL SKA data ( = 0.001Hz) wCDM SKA data ( = 0.001Hz) 0.2 0.4 0.6 0.8 1.0 0.00 0.05 0.10 0.15 0.20 CDM SKA data ( = 0.002Hz) 0.2 0.4 0.6 0.8 1.0 CPL SKA data ( = 0.002Hz) 0.2 0.4 0.6 0.8 1.0 wCDM SKA data ( = 0.00… view at source ↗
Figures from the paper (7 more)
Figure 5
Figure 5. Figure 5: The light blue region in each graph represents the extent of velocity drift, taking into account the uncertainty in H0 ranging from 60 to 80 km/s/Mpc over a 0.5-year ob￾servation period within the redshift interval of 0 to 1. The observed redshift and velocity drift da…
Figure 6
Figure 6. Figure 6: The constraints on the H0 and Ωm parameter space within the 1σ and 2σ confidence intervals, derived from the predicted data utilizing the SKA’s spectral resolutions of 0.001 Hz (blue contours) and 0.002 Hz (green contours). adequate signal-to-noise ratios (S/N >= 100) …
Figure 7
Figure 7. Figure 7: The constraints on w, w0, and wa within the 1σ and 2σ confidence intervals, derived from the forecasted data using the SKA spectral resolutions of 0.001 Hz (depicted by red contours) and 0.002 Hz (depicted by green contours) [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 9
Figure 9. Figure 9: Theoretical velocity variations derived from three distinct models as H0 varies between 60 and 80 km/s/Mpc, depicted within the shallow blue regions. The error bars represent the empirical measurements of redshift drift and velocity drift obtained using the SKA via 21c…
Figure 10
Figure 10. Figure 10: The best-fit value and 1σ(68.3%) and 2σ(95.4%) uncertainties of H0 - Ωm plane from SKA absorption line data under the three cosmological models. et al. 2023; Rao et al. 2017): n(z) = dN/dz = (0.0270.007)(1 + z)(1.682±0.2) (10) The prevalence of Damped Lyman Alpha (DLA…
Figure 12
Figure 12. Figure 12: The 1σ(68.3%) and 2σ(95.4%) confidence level of H0 - Ωm plane constrainted results from SN Ia (red) and BAO data(gray) under the CPL model [PITH_FULL_IMAGE:figures/full_fig_p010_12.png]
Figure 13
Figure 13. Figure 13: The 1σ(68.3%) and 2σ confidence level of constraints on w0-wa plane using SN Ia (red) and BAO data(gray) under the CPL model. 1.76 to -0.09 and wa from -4.84 to 2.79. In comparison to the constrained results derived from 16 BAO data points as referenced in [PITH_FULL…

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