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REVIEW 4 major objections 5 minor 75 references

Disentangling the growth rate of perturbations from the HI bias using only clustering data from galaxy surveys

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that the growth rate of cosmic structure can be measured at selected redshifts using only galaxy clustering data, without external data sets, by locating the turning points of the measurable $f_8(z)$ curve.

desk verdict A clever growth-rate extraction identity that is worth refereeing, but the paper currently demonstrates it robustly only at z1 and has a sign error in its key equation. read the letter →

arxiv 2506.22064 v1 pith:4VQNEMKV submitted 2025-06-27 astro-ph.CO

Pankaj Chavan , Tapomoy Guha Sarkar , Anjan A Sen This is my paper · ORCID
classification astro-ph.CO PACS 98.80.-k
keywords growthratef8redshift-spacedistortionsbaryonacousticoscillations21-cmintensitymappingHIbiasdarkenergycosmicstructure
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 proposes a way to measure the linear growth rate of matter perturbations, $f(z)$, using only clustering data from galaxy surveys, without needing to know the galaxy bias, $\sigma_8$, or external data such as CMB or lensing measurements. The key is that the measurable quantity $f_8(z) = f(z)\sigma_8 D_+(z)$ has a peak at a specific redshift $z_1$, and at that peak its derivative vanishes. At that point, Eq. (5) ties $f(z_1)$ directly to background quantities, the dark-matter fraction $R$ and the dark-energy equation of state $w$, which can be reconstructed from BAO measurements of $H(z)$ and $D_A(z)$. The same logic is applied to a higher-derivative function $F_2$ to get $f$ at a second redshift $z_2$. If this works, 21-cm intensity-mapping surveys can then convert measured redshift-space distortion parameters into a measurement of the poorly known neutral-hydrogen bias.

What carries the argument

The central object is a hierarchy of functions $F_m$ built from logarithmic derivatives of $f_8(z)$; $F_1 = d\ln f_8/d\ln a$ and $F_2 = d\ln F_1/d\ln a + F_1$ are the first two members. The load-bearing identity is that at any redshift $z_m$ where $F_m=0$, the inverse growth rate $\xi = 1/f$ satisfies a polynomial equation whose coefficients depend only on background quantities $R$, $w$, and their derivatives, not on bias or $\sigma_8$. This converts the problem of measuring $f$ from shape information in clustering data into a purely geometric calculation once the zero-crossing redshift is located.

What would settle it

Reconstruct $f_8(z)$ from a larger independent dataset without assuming a fitting form, locate the peak redshift, and compare the value $f(z_1)$ obtained from Eq. (5) with a direct measurement from peculiar velocities or lensing; disagreement beyond the joint error bars would falsify the derivative-zero assumption.

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Extended reading notes

Core claim

The paper's central discovery is that zero crossings of logarithmic derivatives of the observable $f_8(z)$ act as anchor points where the growth rate $f(z)$ can be computed from background cosmology alone. At the peak redshift $z_1$, the condition $F_1 = d\ln f_8/d\ln a = 0$ gives $f(z_1)^{-1} = w(z_1) + (1/3 - w(z_1))/R(z_1)$, with $R$ the matter fraction of the expansion rate and $w$ the dark-energy equation of state, both recoverable from BAO measurements of $H(z)$ and $D_A(z)$. The second logarithmic derivative $F_2$ provides a second zero at $z_2$, where $f(z_2)$ solves an algebraic equation in the background quantities. Once $f(z)$ is known at these redshifts, a measured RSD parameter $\beta_T$ in 21-cm intensity maps directly yields the neutral-hydrogen bias $b_T = f/\beta_T$.

Load-bearing premise

The constructions assume that the measured $f_8(z)$ curve is smooth enough for its turning points to be located from derivatives; the paper's own two fits disagree on the second turning point ($z_2\simeq1.16$ versus $1.78$) and show a $2.5\sigma$ overall tension, so the reliability of the turning-point identification is the load-bearing premise.

Editorial extensions

If this is right

  • At the peak of $f_8$, the growth rate $f(z_1)$ is fixed by the expansion history alone, so a survey that measures $f_8$, $H$, and $D_A$ around that peak can report a bias-free $f(z_1)$ without CMB or weak-lensing input.
  • The higher-derivative condition $F_2=0$ supplies a second growth-rate anchor $f(z_2)$, extending the method beyond the single peak.
  • For 21-cm intensity mapping, the known $f(z)$ at these redshifts converts a measured $\beta_T$ into a direct constraint on the large-scale H I bias $b_T$.
  • Because only the shape of $f_8$ near its turning points matters, the measurement is robust to the overall amplitude of $f_8$, where bias and $\sigma_8$ uncertainties normally hide.
  • More precise $f_8$ data from upcoming surveys will reduce the uncertainty in the zero-crossing redshifts and, hence, in $f(z_1)$ and $f(z_2)$, making the method a test of dark energy versus $\Lambda$CDM.

Reading between the lines

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

  • Applying the same derivative-zero logic to higher functions $F_m$ should yield additional redshifts where $f(z)$ is fixed by background quantities, but the rapidly growing reconstruction errors at higher derivative order will likely limit practical use to $F_2$ with current data.
  • A self-contained version of the pipeline that calibrates the sound horizon from the BAO feature itself, rather than from a prior, would test whether the 'clustering only' claim survives without external input.
  • Foreground removal in 21-cm surveys removes the lowest-$k$ modes, so the projected bias uncertainty of roughly $\pm0.68$ is an optimistic limit; repeating the Fisher forecast with a foreground wedge should show whether the bias constraint remains useful.
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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 / 5 minor

Summary. The paper proposes a method to extract the linear growth rate f(z) at selected redshifts from galaxy clustering data alone, i.e. from RSD measurements of f8(z) and BAO measurements of the background. The central idea is to write F1 = d ln f8/d ln a and F2 = d ln F1/d ln a + F1 in terms of f, the matter-density fraction R(z), and the dark-energy equation of state w(z). At redshifts where these functions vanish, f can be expressed through background quantities only. The authors apply the method to current f8 compilations, recovering f(z1=0.42) ~ 0.7 in both of their reconstruction schemes, and then use this to forecast constraints on the post-reionization 21-cm bias with an SKA1-Mid-like survey. The paper also identifies a second redshift z2 where f could be reconstructed, but the two reconstructions disagree strongly there.

Significance. If the method is validated, it is an elegant and genuinely parameter-free route to f(z) that bypasses the usual need to know the tracer bias or sigma8 separately. The recovered f(z1) agreeing with LCDM is a positive sign, and the phase-space relation in Eq. (4) is a clean analytical result. The main strengths are the simplicity of the central identity and the fact that the turning point of f8(z) is located from the shape of the data rather than fitted to a cosmological model. However, the paper does not provide a mock-based validation of the derivative-zero reconstruction, and the second zero is not robustly located with current data. The 21-cm forecast is also too weak to support the wording 'measure the 21-cm bias', and the abstract's claim of requiring no other data sets is not met in the implementation because a CMB sound-horizon prior is used.

major comments (4)
  1. [Formalism, Eq. (5)] Equation (5) as printed contains a sign error. Setting F1 = 0 in Eq. (4) gives f(z1)^{-1} = w + (1/3 - w)/R, not w + (w - 1/3)/R. With Planck-like LCDM parameters at z ~ 0.42 the printed formula gives a negative f, while the values quoted in Fig. 4 (0.718 and 0.690) correspond to the corrected sign. Please fix the equation and the surrounding derivation, and state explicitly which sign was used in the numerical code.
  2. [Results and Discussion, Fig. 2] The second zero of the derivative hierarchy is not robustly determined: the direct polynomial fit gives z2 = 1.159(+0.818,-0.198) while the semi-cosmographic fit gives z2 = 1.782(+0.161,-0.151), with corresponding f(z2) = 1.083 versus 0.919. The paper acknowledges the large errors, but this is the load-bearing step for the multi-redshift claim. A mock or simulation-based demonstration is needed to show that the zero-derivative redshifts are recovered without bias from realistic f8 data. Without such validation, the method is convincingly demonstrated only at z1.
  3. [Abstract and Results] The claim that f(z) can be obtained 'without requiring any other data sets' is not met in the implementation. Case II uses CMBR priors on the sound horizon rd, and the background quantities are reconstructed from SDSS IV BAO/RSD data with their covariance. Since BAO measurements provide only rd-scaled distances, an external calibration of rd enters the analysis. Please state the minimal external inputs explicitly and temper the abstract accordingly.
  4. [Results, 21-cm forecast] The projected constraint on the 21-cm bias, bT(z=0.42, k<0.01 Mpc^{-1}) = 0.757 +/- 0.682, has an uncertainty comparable to the fiducial value and is therefore not a measurement of the bias. The statement that the method 'allows us to measure the 21-cm bias' is too strong; at best this is a weak bound under optimistic assumptions (foregrounds fully removed, 1000 h observation). Please rephrase or present joint constraints that reflect the actual constraining power.
minor comments (5)
  1. [Throughout] There are several typographical errors: 'bayron' should be 'baryon', 'Cramar-Rao' should be 'Cramer-Rao', and 'due to he availability' should be 'due to the availability'.
  2. [Figure 2 caption] The caption lists 'F2 Direct fit' twice, making the legend ambiguous; please clarify which curve corresponds to F1 and which to F2 in each reconstruction.
  3. [Results, 21-cm section] The notation '1420 MHz (1+z1,2) = 1000 MHz, and 510.42 MHz' is confusing; it should be written as nu_i = 1420 MHz / (1+z_i).
  4. [Methods / MCMC] The paper does not report the MCMC details for either reconstruction: priors, number of walkers/steps, convergence criteria, and the exact data sets used in Case I. Without these, the quoted 1-sigma intervals on z1, z2 and f(z1) cannot be reproduced from the text.
  5. [Companion papers] The semi-cosmographic reconstruction relies heavily on the authors' companion papers [53,57]. A brief summary of the priors and of how the SDSS IV data enter those reconstructions would make this manuscript more self-contained.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central result Eq. (5) fixes f at the f8 turning point from background quantities; f8 data are used only to locate the zero of F1, and no fitted f(z) value is recycled as a prediction.

full rationale

The central claim rests on the identity F1 = d ln f8/d ln a = (3/2)[R(ξ − w) + (w − 1/3)] with ξ = 1/f, derived from the standard linear growth equation and the definition f8 = f σ8 D+. At F1 = 0, Eq. (5) gives f(z1)^{-1} = w + (w − 1/3)/R, which depends only on background quantities R and w evaluated at the turning point. The amplitude of f8 cancels identically, so the method does not fit f(z1) from the f8 data; it only uses the reconstructed f8 shape to locate the peak. Case I is an explicitly model-agnostic polynomial/rational fit to f8, and f(z1) is not a fitted parameter of that fit. Case II uses the authors' prior semi-cosmographic reconstruction [53,57], but the dynamical system is stated in the paper and the central identity is not imported from those references; moreover Case I provides an independent, self-contained demonstration. The paper openly reports that the F2-based second turning point is poorly determined (z2 = 1.159 versus 1.782) and that Case II assumes a CMB prior on rd; these are validation and implementation weaknesses, not circularity. No derivation step reduces to its inputs by construction, and no fitted parameter is renamed as a prediction. Hence no circular step is identified.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The method introduces no new physical entities. It relies on standard linear-theory assumptions, on the authors' phase-space formulation from prior self-cited work, on a CMB prior for the BAO standard ruler, and on fit parameters for the f8 reconstruction. The central relation f(z1) from F1=0 is parameter-free once R and w are known, but the practical implementation depends on the listed assumptions and fitted background parameters.

free parameters (3)
  • f8 rational fit coefficients = A0, A1, A2, B1, B2 (values not reported)
    Case I: f8(z) = (A0 + A1 z + A2 z^2)/(1 + B1 z + B2 z^2) is fit to 70 f8 data points; the peak location z1 depends on these five coefficients.
  • Semi-cosmographic parameters = alpha, beta, gamma, H0, Omega_m0, sigma_8,0 (not tabulated)
    Case II: the background and growth equations are solved with a Padé-based w(z) and fit to SDSS IV (DM/rd, DH/rd, DV/rd, f8) data.
  • Fiducial 21-cm parameters = beta_T and C_T from ΛCDM and the simulation bias model [48]
    Used to define the fiducial point for the Fisher matrix forecast of the 21-cm bias.
assumptions (5)
  • domain assumption Kaiser formula for redshift-space distortions
    The paper models galaxy and 21-cm redshift-space power spectra as P_s = (1 + β μ^2)^2 P_real (Sec. 1, Eq. 1), valid only in linear theory.
  • domain assumption Standard growth and background dynamical equations (Eq. 3)
    The phase-space system for (x, p, f8) is taken from the authors' companion papers [53,57] and assumes a flat universe with a generic w(z).
  • domain assumption CMB prior on the sound horizon rd
    In Case II, BAO distances are calibrated using CMBR priors on rd, contradicting the abstract's claim that no other data sets are needed.
  • domain assumption Constant neutral fraction x_HI = 2.45e-3
    Used in Eq. 2 for the 21-cm brightness temperature amplitude, following [49,50].
  • domain assumption Linear, scale-independent HI bias on large scales
    The 21-cm bias b_T is treated as redshift-dependent only, although the authors note it is scale-dependent on small scales (Sec. 2).

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Cite this review

Pith. "Pith review of Disentangling the growth rate of perturbations from the HI bias using only clustering data from galaxy surveys." pith.science (2026). https://pith.science/paper/4VQNEMKV

@misc{pith2026250622064,
  author       = {Pith},
  title        = {Pith review of: Disentangling the growth rate of perturbations from the HI bias using only clustering data from galaxy surveys},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4VQNEMKV}},
  note         = {Machine review of arXiv:2506.22064}
}
abstract

This work serves two-fold purpose. Firstly, we provide an alternative to the traditional method of determining the growth rate of density perturbations $f(z)$. In usual practice, $f(z)$ can not be directly measured from tracer clustering at some redshift without knowledge of the bias. While the bayron acoustic oscillation (BAO) imprint allows the determination of $(D_A(z), H(z))$, redshift space anisotropy (RSD) allows the measurement of a quantity $f_8(z) = f(z) \sigma_{8,0} D_{+}(z)$. To extract $f(z)$ from $f_8(z)$, one usually requires some other data set. We show that precise BAO and RSD measurements in and around some key redshifts themselves can solely reconstruct $f(z)$ without requiring any other data sets. Secondly, we extend this approach to another tracer, namely the post-reionization 21-cm brightness temperature intensity maps. We demonstrate that the measured $f(z)$ from purely redshift space clustering allows us to measure the 21-cm bias, which is a largely unknown quantity. This may help interpret the observed intensity mapping signal in the future.

Figures

Figures reproduced from arXiv: 2506.22064 by the authors.

Figure 1
Figure 1. shows the the reconstruction of f8(z) by two en￾tirely different approaches. In the semi-cosmographic fit, the (H, DA, f8) data from SDSS IV is used to fit model parame￾ters, while in the other case, all available f8 data is directly fitted with a fitting function. In this work, we propose a method by which f(z) can be measured at some specific fixed redshifts, only using galaxy clustering data. We show that using t… view at source ↗
Figure 3
Figure 3. Demonstrating the graphical method to find roots [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 2
Figure 2. shows functions F1(z) and F2(z) reconstructed us￾ing both semi-cosmographic and direct fitting method. The zero crossings z1 and z2 of these functions are marked re￾spectively. While the slope reconstruction allows a better identification of z1, there are large errors in z2 due to a poor reconstruction of the double derivative. knowledge of the redshifts where Fm(z) vanishes. The overall magnitude of f8 has no beari… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: The reconstruction of f(z) at two redshifts with 1σ error bars. The theoretical behaviour of f(z) for the ΛCDM model with SDSS IV and Planck 18 fit parameters is also shown. the form f8(z) = (A0+A1z+A2z 2 )(1+B1z+B2z 2 ) −1 . In this approach, we are not interested in …

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