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REVIEW 4 major objections 4 minor 92 references

Exploring the signature of assembly bias and modified gravity using small-scale clusterings of galaxies

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

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Pith's one-line read Small-scale galaxy clustering can expose modified gravity with a single velocity-rescaling parameter, provided assembly-bias parameters are included in the model.

desk verdict Solid assembly-bias warning from well-controlled mocks, but the MG 'recovers truth within 1 sigma' claim rests on an unvalidated HOD-weighted calibration. read the letter →

arxiv 2506.22737 v1 pith:AMCODJKQ submitted 2025-06-28 astro-ph.CO astro-ph.GA

Yirong Wang , Zhongxu Zhai , Xiaohu Yang , Jeremy L. Tinker This is my paper · ORCID
classification astro-ph.COastro-ph.GA
keywords galaxyclusteringassemblybiasmodifiedgravityhalooccupationdistributionvelocityemulatorredshift-spacedistortionsgrowthrate
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 argues that a single empirical parameter, $\gamma_f$, which rescales the amplitude of halo peculiar velocities relative to the general-relativistic prediction, can carry two tasks in small-scale galaxy clustering analysis. Jointly fitting $\Omega_m$, $\sigma_8$, and $\gamma_f$ to mock clustering from 0.1 to 60 $h^{-1}$Mpc recovers the true input cosmology within $1\sigma$ only when the emulator model includes environment-dependent assembly bias; when assembly bias is present in the mocks but left out of the model, $\Omega_m$ and $\sigma_8$ are biased and $\gamma_f$ can shift by up to $5\sigma$. Applied to modified-gravity simulations of the DGP and $f(R)$ families, the same parameter departs from unity for the strongest models, DGP-N1 and $f(R)$-F4, and after calibrating with the halo velocity-dispersion ratio it recovers an effective $\gamma_f$ with less than $1\sigma$ residual bias. If correct, this gives observers a one-parameter route to flag modified gravity at nonlinear scales and a quantitative warning about how badly unmodeled assembly bias can distort cosmological inference.

What carries the argument

The load-bearing object is the halo velocity bias parameter $\gamma_f$ (Equation 10), defined as $f/f_{\rm GR}$, which multiplies the amplitude of the halo velocity field in the emulator; a fractional change in $\gamma_f$ tracks a fractional change in $f\sigma_8$ and in the peculiar-velocity amplitude. Around it sit the environment-dependent assembly-bias extension of the HOD (Equation 9), in which the central-galaxy mass scale $M_{\rm min}$ is modulated by the halo's environment overdensity $\delta$ within $10~h^{-1}$Mpc through an error-function term with amplitude $f_{\rm env}$, threshold $\delta_{\rm env}$, and width $\sigma_{\rm env}$; and the velocity-dispersion ratio $\sigma_{\rm MG}/\sigma_{\rm GR}$ measured from the modified-gravity simulations, averaged over $10^{12}$–$10^{15}~h^{-1}M_\odot$ halos, which supplies the effective true $\gamma_f$ for the recovery test. The analysis pipeline is a Gaussian-process emulator of small-scale clustering statistics with a nested-sampling likelihood and a covariance built from jackknife sample variance scaled to the survey volume plus emulator error.

What would settle it

Recompute the effective true $\gamma_f$ for each modified-gravity mock by weighting $\sigma_{\rm MG}/\sigma_{\rm GR}$ by the HOD's host-halo mass distribution for that mock; if the recovered $\gamma_f$ differs from this HOD-weighted truth by more than $1\sigma$ for DGP-N1 or $f(R)$-F4, the single-parameter velocity model is not actually recovering the mock's velocity field.

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Extended reading notes

Core claim

The central claim is that $\gamma_f = f/f_{\rm GR}$, a single multiplicative rescaling of the halo velocity field inside an HOD-based emulator, is a sufficient diagnostic for both assembly-bias systematics and modified gravity. For general-relativity mocks, fitting the projected correlation function $w_p$ and the monopole and quadrupole $\xi_0$, $\xi_2$ over small scales recovers $\Omega_m$, $\sigma_8$, and $\gamma_f$ within $1\sigma$ whenever the model includes the environment-dependent assembly-bias parameters; omitting them when the mock contains assembly bias degrades the recovery, with $\gamma_f$ off by up to $5\sigma$ for some HOD models and the bias in $f\sigma_8$ growing with the assembly-bias-induced clustering deviation near $10~h^{-1}$Mpc. For modified-gravity mocks, $\gamma_f$ moves away from unity by an amount that tracks the strength of the fifth force — noticeably for DGP-N1 and $f(R)$-F4, mildly for the closer-to-GR N5 and F6 — and after applying the mean halo velocity-dispersion ratio $\sigma_{\rm MG}/\sigma_{\rm GR}$ over halo masses $10^{12}$–$10^{15}~h^{-1}M_\odot$ as a calibration, the recovered $\gamma_f$ matches the effective truth with residual bias below $1\sigma$. The paper reads this as showing that one velocity-scaling parameter can both expose assembly-bias-induced errors in growth-rate measurements and identify modified gravity through the enhanced velocity field it generates.

Load-bearing premise

The load-bearing premise is that each modified-gravity model's velocity field can be compressed into a single mass-independent factor $\gamma_f$, with the true value taken as the unweighted mean of the halo velocity-dispersion ratio over $10^{12}$–$10^{15}~h^{-1}M_\odot$ halos even though that ratio changes with halo mass.

Editorial extensions

If this is right

  • If real galaxy samples contain environment-dependent assembly bias, cosmological fits that omit assembly-bias parameters will return biased $\Omega_m$, $\sigma_8$, and $f\sigma_8$ values, with the offset proportional to the assembly-bias-induced clustering deviation near $10~h^{-1}$Mpc.
  • A measured $\gamma_f$ significantly above unity in a massive-galaxy sample would be a small-scale redshift-space signature of the enhanced velocity fields produced by DGP-N1 or $f(R)$-F4 modified gravity.
  • The single-parameter $\gamma_f$ model is sufficient to recover the effective velocity-field amplitude of modified-gravity mocks to better than $1\sigma$ once the halo velocity-dispersion ratio is used for calibration.
  • Adding assembly-bias degrees of freedom does not change the $\gamma_f$ constraint, indicating that the two effects are weakly degenerate in these tests.
  • The emulator-based pipeline can be applied directly to current galaxy surveys to search for both assembly bias and modified-gravity signatures at nonlinear scales.

Reading between the lines

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

  • The paper's 'true' $\gamma_f$ for each modified-gravity model is an unweighted mean of $\sigma_{\rm MG}/\sigma_{\rm GR}$ over a halo-mass range, even though that ratio varies with mass; weighting the average by the HOD's host-halo mass distribution would be a sharper test of whether the recovered $\gamma_f$ really matches the galaxy sample's velocity field.
  • Because the covariance is scaled from a jackknife estimate rather than measured from the mocks themselves, repeating the recovery tests with mock-estimated covariance would show whether the quoted $1\sigma$ and $5\sigma$ thresholds hold.
  • Combining $\gamma_f$ with galaxy-galaxy lensing or higher-order clustering statistics could break the remaining degeneracy between modified-gravity velocity boosts and assembly-bias clustering effects, which the single-probe analysis leaves partially open.
  • The same compression of the velocity field into one parameter could be tested at other redshifts and number densities; the paper expects the conclusions to hold but does not demonstrate it.
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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. The paper uses the Aemulus GR simulation emulator, extended with a halo-velocity scaling parameter gamma_f (Eq. 10), to study two questions. First, it asks whether ignoring environment-dependent assembly bias (modeled by fenv, delta_env, sigma_env in Eq. 9) biases cosmological parameters inferred from small-scale galaxy clustering (0.1-60 Mpc/h). In controlled recovery tests with and without assembly bias in the mocks and model (Table 2, cases C1-C4), the authors find that when the model omits assembly bias parameters but the mocks include assembly bias, constraints on Omega_m and sigma_8 are biased and gamma_f can be off by up to 5 sigma, while models including assembly bias recover the input parameters within 1 sigma. Second, the paper applies the same emulator to MG simulations from the ELEPHANT suite (DGP-N1, DGP-N5, f(R)-F4, f(R)-F6) and claims that the fitted gamma_f deviates from unity for the stronger MG models, and that after a velocity-dispersion (VD) correction based on the halo-mass-dependent ratio sigma_MG/sigma_GR, the model recovers an effective true gamma_f with residual bias smaller than 1 sigma. The paper concludes that gamma_f can serve as a diagnostic of modified gravity and that assembly bias must be included in such analyses.

Significance. The assembly-bias recovery tests (Section 4.1) are carefully designed and internally consistent: they use a range of HOD models and seven cosmologies from the Aemulus test simulations, and the conclusion that omitting assembly bias can bias cosmological parameters is supported by the presented posteriors and Bayesian evidence. This is a useful, controlled demonstration with direct implications for small-scale clustering analyses. The MG part is more fragile. The paper proposes gamma_f as a compact signature of modified gravity, which is an interesting and timely idea, but the calibration of the 'true' gamma_f is ad hoc and the claim of minimal bias is not yet established. Strengths of the paper include the use of publicly available simulation suites and a clear description of the emulator framework; however, no code or data products are provided, so the quantitative claims are not independently reproducible. The published version would be strengthened by providing the mock catalogs and analysis scripts, or at least a detailed breakdown of the MG calibration.

major comments (4)
  1. [Section 4.2, Figure 5] The 'effective true gamma_f' used to evaluate the MG recovery residuals is defined as the unweighted mean of sigma_MG/sigma_GR over halo masses 12-15 h^-1 M_sun. Figure 5 itself shows that this ratio is mass-dependent, rising from about 1.0 to roughly 1.15 toward the massive end. Since the mock galaxies are CMASS-like and preferentially occupy halos above 10^13 h^-1 M_sun, the HOD-weighted average velocity boost can differ from the unweighted mean. The paper states that a more accurate HOD-weighted correction would give a 'minor' difference, but no calculation is provided. Because the headline claim of sub-1-sigma residual bias in Figure 4 is measured against this constructed truth, a shift of only the quoted 1-sigma uncertainty in the calibration would change the conclusion. Please compute the HOD-weighted sigma_MG/sigma_GR for each mock and re-evaluate the residuals, or otherwise bound the systematic error in the effective true gamma_f.
  2. [Section 4.2, Eq. (10) and Figure 5] The model assumes a single mass-independent multiplicative parameter gamma_f scaling the entire halo velocity field. Figure 5 shows the MG-induced velocity boost is mass-dependent, so the fitted gamma_f is necessarily a compromise averaged over the scales and HOD weights probed by the clustering data. It is therefore not obvious that gamma_f can be interpreted as 'the underlying strength of the velocity field' of the MG model. To support this interpretation, the paper should validate that the gamma_f-scaled GR velocity field reproduces the scale- and mass-dependent RSD of the MG mocks (e.g., by comparing model and mock wp, xi0, and xi2 residuals across all fitted scales), rather than only checking the posterior mean of gamma_f against a mass-averaged ratio.
  3. [Section 4.2, Figure 4] The text in Section 4.2 says that ten HOD models are selected for the MG analysis, but Figure 4 and Appendix Figure C show results for only five HOD models. This discrepancy matters because the paper's conclusion that the recovery bias is 'not larger than 1 sigma' is based on the displayed subset. If results for the other five HOD models are available, they should be shown, or the text should clarify why only five are presented and whether the remaining five change the conclusions.
  4. [Section 3.2, Eq. (15)] The covariance matrix is scaled from a BOSS-CMASS jackknife estimate with added emulator error, rather than measured from the mock catalogs used in the recovery tests. Since all significance claims (e.g., the 5-sigma gamma_f bias in case C4 and the sub-1-sigma MG residuals) are quoted in units of this covariance, the adequacy of the scaled BOSS covariance for these synthetic samples should be justified. A simple check would be to compare the fractional errors from the mocks themselves with the adopted covariance; if they differ significantly, the quantitative significance levels of the paper's claims need revision.
minor comments (4)
  1. [Figures 1-5] The axis labels in several figures are garbled or incomplete (e.g., Greek letters and math symbols appear as 'uni' sequences and the label for the y-axis of Figure 2 is not rendered). Please regenerate the figures with proper LaTeX/mathtext labels so that the panels are readable.
  2. [Section 2.2.1, Eq. (3)] The definition of f(R) in Eq. (3) would benefit from an explicit statement of the sign convention and a reference to the Hu-Sawicki form; also 'c1; c2' should be 'c1, c2'.
  3. [Section 4.2] The sentence 'five cosmological parameters, namely Omega_b, h, n_s, omega, and Neff, are fixed' is unclear: the symbol 'omega' is not defined in this context (presumably Omega_m h^2 or the baryon density parameter?). Please specify the exact parameters and their fixed values.
  4. [References] References Zhai et al. 2023a and Zhai et al. 2023b appear to have identical bibliographic details (MNRAS, 523, 5538); please check whether these are distinct papers or a duplicate citation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the assembly-bias and modified-gravity tests are emulator closure and calibration checks against external simulations; the effective true gamma_f is a constructed calibration target, not a definitionally forced identity.

full rationale

The emulator analysis is a sequence of recovery tests: mocks are generated from Aemulus GR simulations or external ELEPHANT MG simulations, and the emulator with gamma_f and assembly-bias parameters is fit to their clustering (Eq. 14). Recovering the input cosmological parameters in cases C1-C3 is a closure test, and the biased recovery in C4 is a substantive demonstration that a misspecified galaxy-halo connection shifts Omega_m, sigma_8, and gamma_f. Nothing in these steps is defined in terms of the output, and no fitted parameter is renamed as a prediction. On the MG side, gamma_f (Eq. 10) is a free velocity-amplitude scaling, and the effective true gamma_f for each MG model is separately constructed as the mean halo velocity-dispersion ratio sigma_MG/sigma_GR over 12 <= log10 M <= 15 (Fig. 5). The fitted gamma_f is not algebraically forced to equal this ratio; the agreement reported in Fig. 4 is a genuine, though model-dependent, calibration check. The unquantified statement that an HOD-weighted correction would differ only mildly, together with the paper's selection of 10 HOD models while Fig. 4 shows five, weakens the robustness of the <1-sigma claim, but these are validation gaps rather than circular reductions. The covariance matrix is scaled from BOSS-CMASS jackknife estimates rather than measured from the mocks, which affects error estimation but not the logical direction of the derivation. Self-citations to Zhai et al. (2019, 2023c) and Reid et al. (2014) motivate the empirical gamma_f ansatz, but the parameter is tested against independent simulations; no uniqueness theorem or prior conclusion is imported to forbid alternatives. Thus no step exhibits Eq. X = Eq. Y by construction or a fitted quantity relabeled as a prediction; the paper is self-contained against external benchmarks, and the circularity score is 0.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

No fundamentally new physical entities are introduced. The analysis relies on an existing galaxy halo connection model, an existing velocity scaling parameter, and external MG simulations; the main ad hoc inputs are the environment based assembly bias parametrization and the velocity dispersion based calibration of the true gamma_f.

free parameters (5)
  • gamma_f (halo velocity bias scaling) = posterior constrained values; near 1 for GR, above 1 for DGP-N1 and F4
    Central fitted parameter: defines the MG signature when it deviates from unity. Fitted to wp, xi0 and xi2 in each recovery test.
  • f_env, delta_env, sigma_env (assembly bias parameters) = varied with priors; not quoted numerically
    Control environment dependent M_min scaling in Eq. 9. Included in model scenarios C1, C3 and TT; when set to zero, assembly bias is ignored.
  • VD correction ratio <sigma_MG/sigma_GR> = around 1.15 for the strongest MG model
    Computed from halo velocity dispersions in the 12 to 15 h^-1 M_sun range and used as the effective true gamma_f for MG models; a post hoc calibration of the truth.
  • HOD parameters (M_min, M_sat, alpha, M_cut, sigma_logM, ngal, eta_con, eta_vc, eta_vs) = varied per fit
    Galaxy halo connection parameters varied in the likelihood; their degeneracies with gamma_f determine the claimed constraints.
  • proxy scale 10 h^-1 Mpc = fixed at 10 h^-1 Mpc
    Chosen by hand to quantify assembly bias strength via Delta xi/xi; the paper states other scales do not change conclusions.
assumptions (6)
  • domain assumption HOD prescription (Zheng et al. 2005; Zhai et al. 2019) is a valid galaxy halo connection for CMASS-like samples
    Used to generate all mock catalogs; if the true galaxy halo connection differs, recovery tests could be biased.
  • domain assumption Environment based assembly bias model (Eq. 9) captures the relevant assembly bias
    Only environment (delta within 10 h^-1 Mpc) is used as secondary halo property; other assembly bias proxies may behave differently.
  • ad hoc to paper gamma_f uniformly scales the whole halo velocity field
    Eq. 10 defines gamma_f = f/f_GR as a single scalar; Figure 5 shows the MG/GR velocity dispersion ratio is mass dependent, making this a simplifying assumption.
  • domain assumption Covariance from BOSS-CMASS jackknife scaled to mock volume approximates the mocks' true covariance
    Eq. 15; the mock catalogs have different volumes and HODs, so the scaled covariance is an approximation.
  • ad hoc to paper The average sigma_MG/sigma_GR over 12 to 15 h^-1 M_sun represents the effective true gamma_f
    Used to define the truth for MG models in Figure 4; the paper states the HOD weighted correction is minor but does not demonstrate it.
  • domain assumption The Aemulus emulator is accurate over the parameter space
    Emulator predictions are interpolated from 40 GR simulations; C_emu partially accounts for error.

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Cite this review

Pith. "Pith review of Exploring the signature of assembly bias and modified gravity using small-scale clusterings of galaxies." pith.science (2026). https://pith.science/paper/AMCODJKQ

@misc{pith2026250622737,
  author       = {Pith},
  title        = {Pith review of: Exploring the signature of assembly bias and modified gravity using small-scale clusterings of galaxies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AMCODJKQ}},
  note         = {Machine review of arXiv:2506.22737}
}
abstract

We apply a halo velocity bias model, $\gamma_{f}$, within the Aemulus simulation suite for General Relativity (GR) to investigate its efficacy in identifying the signature of assembly bias and Modified Gravity (MG). In the investigation of assembly bias, utilizing galaxy clustering data ranging from scales of $0.1 - 60 \text{Mpc}\,h^{-1}$, we discover that our emulator model accurately recreates the cosmological parameters, $\Omega_m$ and $\sigma_8$, along with the velocity bias $\gamma_{f}$, staying well within the 1-$\sigma$ error margins, provided that assembly bias is considered. Ignoring assembly bias can considerably alter our model constraints on parameters $\Omega_m$ and $\sigma_8$ if the test sample includes assembly bias. Using our emulator for MG simulations, which encompasses two Dvali-Gabadadze-Porrati models (DGP; N1, N5) and two $f(R)$ models (F4, F6), we can effectively identify a robust signature of modified gravity, for models such as DGP-N1 and $f(R)$-F4, as indicated by a noticeable deviation of $\gamma_{f}$ from unity. Using the velocity dispersion of dark matter halos to effectively represent the underlying strength of the velocity field of these MG simulations, we find that the simple $\gamma_{f}$ model can recover the truth with minimal bias. These evaluations indicate that our simple halo-velocity bias model is capable of detecting significant MG characteristics, although additional methodologies should be pursued to improve model constraints.

Figures

Figures reproduced from arXiv: 2506.22737 by the authors.

Figure 1
Figure 1. Two examples of the constraints on Ωm, σ8 and γf for two different cosmology and different HOD models. The ‘C1, C2, C3, C4’ for different colors stand for different cases which are listed in [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Bias in the measurement of fσ8 when the model of galaxy clustering at non-linear scale has assembly bias or not. The mocks are produced by the Aemulus test simu￾lations with different HOD models and assembly bias pa￾rameters. In order to denote the strength of assembly bias, for each HOD model we compute the residual of ξi com￾pared with the result when fenv is set to 0, i.e. the assembly bias effect is turned off. … view at source ↗
Figure 3
Figure 3. Two examples of the constraints on Ωm, σ8 and γf for two different HOD models using MG simulations. Different colors in each panel stand for different modified gravity methods which are listed in [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Constraints on γf (upper half of each panel) from unity and Bayesian Evidence (lower half of each panel) for GR and four modified gravity methods with the same cosmological parameter setting at z = 0.55. Five panels correspond to five different HOD models. The errorbar…
Figure 5
Figure 5. Figure 5: Velocity dispersion measured from the MG sim￾ulation compared with the GR result, as a function of halo mass at redshift z = 0.55. Different MG methods are re￾spectively represented by distinct colors. In the calculation of the true value of γf for four MG methods in …

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