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REVIEW 4 major objections 4 minor 43 references

The Hubble constant tension with next-generation galaxy surveys

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper forecasts that next-generation BAO surveys, combined across redshift bands, can measure the Hubble constant to about 1% precision and thereby discriminate between the current early- and late-Universe measurements at roughly 5.6σ.

desk verdict A sensible forecast paper that overstates its own precision and significance by mishandling error units and the quadrature sum. read the letter →

arxiv 1908.04619 v2 pith:OWB6LRBG submitted 2019-08-13 astro-ph.CO

Carlos A. P. Bengaly , Chris Clarkson , Roy Maartens This is my paper · ORCID
classification astro-ph.CO PACS 98.65.Dx98.80.Es
keywords HubbleconstanttensionbaryonacousticoscillationsGaussianprocessregressionSKAintensitymappingEuclidgalaxysurveyH(z)reconstructioncosmologicalforecasts
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

The paper asks how precisely future spectroscopic galaxy surveys can measure the present-day expansion rate H0, and whether that precision can settle the current 4–6σ disagreement between early- and late-Universe measurements. Using forecast baryon acoustic oscillation data from SKA-like intensity mapping and Euclid-like galaxy surveys, the authors simulate H(z) data points and reconstruct the expansion history with Gaussian process regression, which requires no assumed parametric form. Their central result is that combining the low-redshift SKA-like Band 2 with either SKA-like Band 1 or Euclid-like data reaches roughly 1.2% precision on H0 with 40 data points, enough to rule out one side of the current tension at about 5.6σ. If these forecasts hold, the Hubble tension becomes a sharp discriminator between cosmological models rather than a stubborn observational puzzle.

What carries the argument

The load-bearing tool is Gaussian process regression, implemented with the GaPP code, which reconstructs the full function H(z) from discrete data without committing to a cosmological parametrization. Extrapolating the reconstructed function to z=0 yields the Hubble constant, with the uncertainty at z=0 set by the GP covariance and the input error bars. The input errors are the forecast per-redshift uncertainties on H(z) from the SKA Red Book (Figure 10, left), interpolated across each survey's redshift range; those errors, rather than cosmic variance, dominate the predicted H0 precision.

What would settle it

When the first real SKA-like Band 1+2 data deliver about 40 H(z) points, run the same GaPP regression and compare the reconstructed H0 uncertainty to 1.2%; in parallel, run a coverage test on simulated surveys by drawing many fiducial H0 values and checking that the GP 68% band at z=0 contains the true value in about 68% of realisations.

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Extended reading notes

Core claim

The central claim is that a non-parametric Gaussian-process regression of forecast H(z) measurements from next-generation BAO surveys can recover H0 at z=0 with precision close to 1%, and that this precision is sufficient to distinguish the two mutually incompatible H0 values currently measured from the early and late universe at approximately 5.6σ. Specifically, combining SKA-like Band 1 (30 data points at 0.35<z<3.06) with Band 2 (10 points at 0.1<z<0.5) gives σH0/H0 = 1.20%, and the same combination of SKA-like Band 2 with Euclid-like data gives 1.29–1.37% depending on the number of Euclid points. The recovered H0 uncertainty is insensitive to the fiducial H0 adopted and remains robust under changes in the assumed dark-energy model and the Gaussian-process covariance kernel.

Load-bearing premise

The forecast inherits the SKA Red Book's per-redshift H(z) error bars, and if those are even 30% optimistic—or if the Gaussian-process extrapolation to z=0 is biased—the claimed 1.2% precision and 5.6σ discrimination shrink.

Editorial extensions

If this is right

  • With 40 SKA-like Band 1+2 data points, the predicted H0 uncertainty is about 1.2%, rivaling the precision of the current CMB-based measurement and exceeding the supernova-based one.
  • The same combination discriminates between the early- and late-Universe H0 values at the 5.6σ level, which would effectively settle which measurement is wrong.
  • Combining low-redshift SKA-like Band 2 with high-redshift Euclid-like data reaches 1.3–1.4% precision, so cross-survey combinations are nearly as powerful as a single survey's two bands.
  • Surveys covering only higher redshifts or narrower ranges, such as DESI-like or MeerKAT-like configurations, are forecast to deliver only 5–10% H0 precision, far below what the tension requires.

Reading between the lines

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

  • The same Gaussian-process pipeline could be applied today to existing cosmic-chronometer and BAO data to produce a current best model-independent H0 constraint; the forecast numbers in the paper quantify how much future surveys improve on that.
  • Because the result depends on the interpolated forecast errors from the SKA Red Book, the real deliverable depends on whether intensity-mapping systematics (foreground cleaning, calibration) reach the assumed levels; a 30% degradation in those errors would pull the 5.6σ discrimination down to roughly 3–4σ.
  • If a future 1% H0 measurement lands between the current CMB and supernova values rather than on one of them, the tension framework itself—assuming both are correct—would need revision.
  • The method's model independence means the same H(z) data can also test smooth dark-energy parametrizations; the paper's CPL fits show that parametric fits can be biased when the wrong model is assumed, whereas the GP recovery is not.
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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 / 4 minor

Summary. This paper forecasts the precision with which future galaxy surveys (Euclid-like and SKA-like) can constrain the Hubble constant H0 by reconstructing H(z) from mock BAO measurements and extrapolating to z=0 with Gaussian process regression. Using the public GaPP code, the authors propagate assumed H(z) error curves from Bacon et al. [14] and report relative H0 precisions between about 1.2% and 4%, claiming that combined SKA Band 1+2 observations could distinguish the Planck 2018 and Riess et al. 2019 H0 values at about 5 sigma. The paper also presents robustness tests against alternative dark-energy models, cosmological parameter variations, and GP kernel choices.

Significance. If the reported numbers were correct, this would be a valuable forecast for the ability of next-generation BAO surveys to address the H0 tension with a non-parametric method. The use of a public, tested GP code, the explicit robustness checks, and the comparison with parametric fitting methods are clear strengths. However, the headline quantitative claims rest on two internal normalization and denominator errors that make the reported precision and significance too optimistic; the method itself remains sound, but the central quantitative results need to be recomputed and restated.

major comments (4)
  1. [Section III.A, Table I; Eq. (6)] The column labelled sigma_H0/H0 is computed as 100 times sigma_h with h in units of 100 km/s/Mpc, not as sigma_h/h_fid. For the headline SKA-like B1+B2 row with N=40, the reconstruction error is sigma_rec=0.01199 in h; relative to the P18 fiducial h=0.6736 this is 1.78%, not 1.198%, and relative to the R19 fiducial h=0.7403 it is 1.62%. The same rescaling applies to every row of Table I and to Eq. (9), so the abstract's 'close to 1%' claim and Figure 2's comparison with the P18 and R19 relative error bars are not supported as stated.
  2. [Section II, Eqs. (5)-(6); Section III.A, Table I] Equation (6) defines Trec with only sigma_rec in the denominator, whereas Eq. (5), which is the stated definition of tension between two Gaussian measurements, requires sqrt(sigma(h1)^2 + sigma(h2)^2). Since the two mock reconstructions have the same uncertainty sigma_rec, the denominator in Eq. (6) should be sqrt(2) sigma_rec. Consequently all Trec values in Table I are inflated by a factor sqrt(2); the N=40 SKA B1+B2 row corresponds to T approximately 3.9 rather than 5.6, and the claimed '~5 sigma' discrimination between P18 and R19 is not supported by the paper's own defining formula. This affects the abstract, Section III, and Section IV.
  3. [Section II, data uncertainties; Figure 10 of [14]] The entire forecast is a propagation of the H(z) error curves taken from the left panel of Figure 10 of Bacon et al. [14], but those curves are neither reproduced nor tabulated in the manuscript. Because the GP reconstruction error at z=0 is directly determined by these input error bars, an independent reader cannot check the central result, and the quoted precision is conditional on unstated details of an external forecast. Please provide the interpolated sigma_H(z) function (or a table) and include a sensitivity test, for example scaling the assumed errors by a factor 1.3 and reporting the resulting change in sigma_H0/H0 and Trec.
  4. [Section III.B, robustness tests] The kernel and dark-energy robustness tests do not address whether the GP uncertainty at z=0 is correctly calibrated. The mock data start at z>=0.1 (SKA Band 2) or z>=0.6 (Euclid-like), so sigma_rec depends on extrapolation outside the data range. A Monte Carlo coverage test—simulating many realizations from the fiducial model, reconstructing each with the same pipeline, and checking the fraction of 1-sigma intervals that contain the true H0—would be needed to validate the quoted error. As it stands, the reported precision at z=0 is an assumption of the method rather than a tested result.
minor comments (4)
  1. [Section IV, paragraph on SKA B1+2] The sentence 'reach a precision of 1.2% (1.4%) with 20 (40) total data points' appears to reverse the entries in Table I, which give 1.36% for N=20 and 1.198% for N=40.
  2. [Table I, R19 row] The listed relative uncertainty for R19 is 1.981%, but 1.42/74.03 is 1.92%; please check the source values or the calculation.
  3. [Figure 1 caption] Since the plotted error bars are scaled up by factors of 10 and 6 for visibility, it would be helpful to state the true 1-sigma error of representative data points so the reader can gauge the input assumptions.
  4. [Section II, Eq. (4)] The matter-density prior is quoted with an uncertainty, but the text does not state whether this uncertainty is propagated into the GP reconstruction or whether Omega_m is fixed to its central value; please clarify.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the H0 precision forecast propagates externally assumed survey errors; self-citations are methodological and not load-bearing.

full rationale

The paper's derivation chain is a forward forecast, not a circular reduction. Mock H(z) data are generated from fiducial H0 values (P18 or R19) plus redshift-dependent error curves taken from the SKA Red Book [14], and a Gaussian-process regression extrapolates the reconstructed H(z) to z = 0. The resulting sigma_H0/H0 values in Table I are therefore conditional forecasts that depend on the assumed input errors and redshift coverage, which is standard forecasting practice rather than circularity: the target result (H0 precision) is not used as an input to define the inputs, and the per-redshift errors are taken from an external forecast. The claim that SKA-like Band 1+2 can discriminate P18 from R19 at ~5 sigma is a direct propagation of the reconstructed uncertainty and the fixed fiducial difference; even if the tension formula in Eq. (6) omits the quadrature sum required by Eq. (5), that is a statistical arithmetic error, not a circularity. The self-citations present in the paper (GaPP code [20], the tension definition [27], earlier GP cosmography [17]) are methodological references to standard, publicly available tools and prior results; they are not used to justify the central claim by appeal to an unverified theorem or to forbid alternatives. No fitted parameter is renamed as a prediction, no uniqueness theorem is imported from the authors' prior work, and no ansatz is smuggled in via citation. The paper even tests robustness to kernel choice, cosmological model, and parameter variations, showing that the central forecast is not an artifact of a specially tuned input. The score is therefore 0.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim rests on an externally assumed error budget for H(z) and on the GP's extrapolation behavior. No new physical entities, forces, or parameters are introduced beyond standard cosmological inputs and GP hyperparameters.

free parameters (1)
  • GP kernel hyperparameters (squared exponential amplitude and length scale) = not quoted; optimized via marginal likelihood per mock dataset
    These set the correlation length and variance of the Gaussian process, directly controlling the extrapolated H0 uncertainty. The paper tests Matern kernels but does not report fitted hyperparameters.
assumptions (4)
  • domain assumption The forecast errors on H(z) from Bacon et al. [14] (left panel of Figure 10) are realistic and achievable.
    Every headline precision number is a propagation of these assumed per-redshift errors. If they are optimistic, the forecast H0 precision degrades proportionally.
  • domain assumption The Gaussian process with a squared exponential or Matern kernel provides an unbiased reconstruction of H(z) and a correctly calibrated extrapolation to z=0.
    The quoted H0 uncertainty is the GP posterior variance at z=0. The paper checks kernel robustness but does not run a full Monte Carlo coverage test to confirm that the 1 sigma GP errors contain the true value 68% of the time.
  • domain assumption The fiducial flat LambdaCDM model (Eq. 3) with Omega_m = 0.3166 ± 0.0084 generates realistic mock H(z) data.
    Mock data are drawn from this model. The authors test wCDM and CPL variations and find small changes, but the baseline forecast assumes LambdaCDM.
  • standard math The tension measure in Eq. (5) for 1D Gaussian distributions applies to reconstructed H0 values.
    Standard error propagation for the difference of two independent Gaussian measurements, as used throughout the tension literature.

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Cite this review

Pith. "Pith review of The Hubble constant tension with next-generation galaxy surveys." pith.science (2026). https://pith.science/paper/OWB6LRBG

@misc{pith2026190804619,
  author       = {Pith},
  title        = {Pith review of: The Hubble constant tension with next-generation galaxy surveys},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OWB6LRBG}},
  note         = {Machine review of arXiv:1908.04619}
}
abstract

The rate at which the universe is expanding today is a fundamental parameter in cosmology which governs our understanding of structure formation and dark energy. However, current measurements of the Hubble constant, $H_0$, show a significant tension ($\sim 4-6\sigma$) between early- and late-Universe observations. There are ongoing efforts to check the diverse observational results and also to investigate possible theoretical ways to resolve the tension~-- which could point to radical extensions of the standard model. Here we demonstrate the potential of next-generation spectroscopic galaxy surveys to shed light on the Hubble constant tension. Surveys such as those with Euclid and the Square Kilometre Array (SKA) are expected to reach sub-percent precision on Baryon Acoustic Oscillation (BAO) measurements of the Hubble parameter, with a combined redshift coverage of $0.1<z<3$. This wide redshift range, together with the high precision and low level of systematics in BAO measurements, mean that these surveys will provide independent and tight constraints on $H(z)$. These $H(z)$ measurements can be extrapolated to $z = 0$ to provide constraints on $H_0$ using a non-parametric regression. To this end we deploy Gaussian processes and we find that Euclid-like surveys can reach $\sim$3\% precision on $H_0$, with SKA-like intensity mapping surveys reaching $\sim$2\%. When we combine the low-redshift SKA-like Band 2 survey with either its high-redshift Band 1 counterpart, or with the non-overlapping Euclid-like survey, the precision is predicted to be close to 1\% with 40 $H(z)$ data points. This would be sufficient to rule out the current early- or late-Universe measurements at a $\sim$5$\sigma$ level.

Figures

Figures reproduced from arXiv: 1908.04619 by the authors.

Figure 1
Figure 1. FIG. 1. Gaussian-process reconstructed [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Compilation of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Marginalised likelihood for the parameter [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.