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The Millennium and Astrid galaxies in effective field theory: comparison with galaxy-halo connection models at the field level

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read This paper shows that red and blue galaxies in two large hydrodynamic simulations are accurately described by the field-level EFT model, with measured bias parameters matching the halo-occupation models used in survey analysis.

desk verdict Solid field-level validation of HOD/HMQ against hydro galaxies, with a same-epoch gap in the ELG vs LRG-HOD comparison that should be fixed. read the letter →

arxiv 2412.01888 v1 pith:IAASVOE6 submitted 2024-12-02 astro-ph.CO

Mikhail M. Ivanov , Carolina Cuesta-Lazaro , Andrej Obuljen , Michael W. Toomey , Yueying Ni , Sownak Bose , Boryana Hadzhiyska , César Hernández-Aguayo
show 3 more authors
Lars Hernquist Rahul Kannan Volker Springel
This is my paper · ORCID
classification astro-ph.CO
keywords effectivefieldtheoryoflarge-scalestructuregalaxybiashalooccupationdistributionhighmassquenchedmodelMillenniumTNGAstridsimulationredshift-spacedistortionsfield-levelforward
open problems Dark Matter
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 tests whether the empirical halo-based recipes used to model galaxy clustering survive a harder test: comparing the full galaxy density field, not just the two-point function. Using the MillenniumTNG and Astrid hydrodynamic simulations, the authors select BOSS/DESI-like LRGs at z=0.5 and DESI-like ELGs at z=1, fit their fields with an EFT forward model, and compare the resulting bias and counterterm parameters with HOD and HMQ model distributions. They find that LRG parameters are consistent with LRG-HOD priors, while ELG local bias parameters are consistent with the HMQ model but not with LRG-like HOD models. They also find that ELGs show weaker fingers-of-God, which would make more of their data usable in perturbative analyses. If correct, this validates the halo-based priors used in full-shape cosmological analyses and extends them to the field level.

What carries the argument

The argument is carried by the field-level EFT forward model, which builds the galaxy density field from shifted bias operators (Zel'dovich-displaced linear density, tidal, and Galileon operators) and extracts transfer functions beta_i(k) directly from simulation snapshots, cancelling cosmic variance. These transfer functions are fitted with time-sliced perturbation theory to yield EFT bias parameters and redshift-space counterterms. The comparison side uses HOD and HMQ galaxy catalogs generated on the AbacusSummit small suite, processed with the same forward-model pipeline, and a normalizing flow trained on paired HOD-EFT samples converts measured EFT parameters back into inferred HOD parameter distributions.

What would settle it

Fit the full-shape power spectrum and bispectrum of DESI ELG data and measure b1 and b2: if b2 falls on the LRG-HOD relation rather than near the dark-matter halo curve, the paper's HMQ consistency claim and its HOD-weighting explanation for ELG bias would be wrong.

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Extended reading notes

Core claim

The paper establishes that the EFT-based field-level forward model accurately reproduces the large-scale density fields of hydrodynamic galaxies, and that the EFT parameters extracted from MTNG and Astrid match the predictions of the phenomenological halo-based models currently used for cosmological surveys. For red galaxies the match is to the decorated HOD models; for blue galaxies the match is to the HMQ model, which the paper shows reproduces both the anomalous local bias parameters and the weak fingers-of-God of ELGs. The authors also provide an analytic argument: the quadratic bias b2 of a galaxy sample is the HOD-weighted average of halo b2, so the shape of the HOD and the halo mass function determine whether galaxies lie above the halo b2(b1) curve, as LRGs do, or on it, as ELGs do.

Load-bearing premise

The comparison treats galaxies selected by a specific star formation rate threshold at fixed number density as stand-ins for the observed BOSS LRGs and DESI ELGs; if those cuts do not faithfully match how surveys actually select these galaxies, the measured EFT parameters and the HOD/HMQ validation would not transfer to real data.

Editorial extensions

If this is right

  • LRG-HOD priors used in EFT full-shape analyses of BOSS are robust to replacing halo mocks with hydrodynamic galaxies on quasi-linear scales.
  • The HMQ model can serve as a simulation-based prior for DESI ELG full-shape analyses, including higher-order bias parameters.
  • Because ELG fingers-of-God are weaker, the maximum wavenumber usable in ELG perturbative analyses can be larger, giving full-shape fits more usable modes.
  • The normalizing-flow mapping provides a cheap way to calibrate HOD parameters to reproduce the field-level clustering of hydrodynamic galaxies, and can be rerun for any new simulation or galaxy selection.
  • EFT parameter responses to selection cuts are not universal; they depend on the baryonic feedback model, so feedback must be controlled before using such priors blindly.

Reading between the lines

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

  • An implication the authors leave implicit: if the weak ELG fingers-of-God are real, DESI's ELG sample could yield cosmological constraints comparable to or better than LRGs despite lower bias, because more modes enter the perturbative regime; this is directly testable with the DESI full-shape pipeline.
  • The b2(b1) distinction between LRG-like and ELG-like populations could be used as a data-driven diagnostic of the galaxy-halo connection: measuring b1 and b2 jointly in survey data tells you whether a target sample behaves like a thresholded high-mass HOD or a narrow-mass HOD without needing small-scale clustering.
  • A testable extension of the paper's logic is to build a suite of cosmological hydrodynamic simulations with varied subgrid feedback, which would quantify how much EFT parameter priors spread across plausible galaxy formation models and could then be marginalized over.
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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

3 major / 5 minor

Summary. The paper measures the effective field theory (EFT) bias parameters and redshift-space counterterms for LRG and ELG samples selected from the MillenniumTNG (MTNG) and Astrid hydrodynamic simulations, and compares them with the corresponding quantities extracted from HOD (LRG) and HMQ (ELG) mock catalogs at the field level. The authors report that LRG EFT parameters are consistent with previous LRG-HOD priors, that ELG local bias parameters are in tension with LRG-like HOD models but consistent with the HMQ model, that ELGs show weaker fingers-of-God, that the response to sSFR cuts differs between MTNG and Astrid owing to feedback modeling, and finally that normalizing-flow-based conditional distributions can map measured EFT parameters to optimal HOD/HMQ parameters.

Significance. If the results hold, the paper provides a valuable field-level validation of halo-based galaxy-halo connection models for both red and blue galaxies, directly supporting the use of HOD/HMQ-based priors in EFT full-shape cosmological analyses. The comparison across two independent hydrodynamic simulations with different feedback implementations is a genuine strength, as is the use of the publicly available Hi-Fi mocks code and the explicit field-level cross-correlation analysis. The finding that ELG local bias parameters deviate from LRG-HOD predictions, if confirmed at matched redshift, would have practical implications for ELG analyses.

major comments (3)
  1. [Section 3.3 and Section 2, item 3] The central claim that ELG local bias parameters are in 'very strong tension' with LRG-based HOD models compares MTNG/Astrid ELG measurements at z=1 (Section 3.2) with LRG-HOD prior distributions generated at baseline redshift z=0.5 (explicitly stated in Section 3.3). Bias parameters evolve with redshift and the halo mass function at fixed HOD parameters changes between z=0.5 and z=1, so the prior distribution of EFT parameters for the same HOD priors need not be the same at z=1. The HMQ baseline z=1.1 is also not exactly z=1. Please add a same-epoch comparison, for example by generating LRG-HOD mocks at z=1 or by mapping the z=0.5 prior distributions to z=1 using the growth factor and mass function, and demonstrate that the conclusion is unchanged.
  2. [Section 3.4] Astrid redshift-space EFT fits use kmax=0.4 h/Mpc in both real and redshift space, whereas MTNG and the HOD/HMQ mocks use kmax=0.2 h/Mpc for redshift-space transfer function fits. Since redshift-space counterterms are known to be sensitive to the scale cut, the reported consistency of Astrid counterterms with HOD/HMQ priors in figs. 7 and 10 could be affected by the different cutoff. Please provide Astrid redshift-space results at kmax=0.2 h/Mpc or explicitly demonstrate that the counterterm constraints are stable when kmax is varied between 0.2 and 0.4 h/Mpc.
  3. [Section 4.3, Eqs. (25)-(29)] The analytic argument explaining the enhanced b2 of LRGs relative to halos is derived under a Heaviside central HOD, no satellites, and a Press-Schechter mass function. Since the abstract advertises this argument as explaining the ELG versus LRG-HOD phenomenology, please validate the derivation against the actual HOD/HMQ weighting functions used in the mock catalogs, for example by direct numerical evaluation of Eq. (25) for the LRG-HOD-I, LRG-HOD-II, and HMQ parameter samples, to show that the simplifying assumptions do not drive the conclusion.
minor comments (5)
  1. [Section 3.2] The text states that 'the SFR cut selection provides a good approximation to samples of [OII] emitting galaxies' and refers to [62]; please add a brief caveat that this is an approximation and that the color-based selection is not used in the analysis, as the authors themselves note.
  2. [Section 4.1] The phrase 'sub Poisson stochasticity' should read 'sub-Poissonian stochasticity' for grammatical correctness.
  3. [Section 4.2] The sentence 'Astrid ELGs do not response monotonically to lowering of sSFR' contains a typo: 'response' should be 'respond'.
  4. [Section 4.4] When describing the HMQ normalizing-flow training, the paper says that αs and αc are excluded from the training sample; please clarify why these velocity bias parameters are excluded for ELG inference while they are included in the HMQ prior definition in Eq. (11).
  5. [Figures 1 and 2] The captions should state explicitly that the LRG-HOD distributions are at z=0.5, the HMQ distributions at z=1.1, and the hydro galaxy measurements at z=0.5 (LRGs) and z=1 (ELGs), to avoid reader confusion about the redshift baselines.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the EFT parameter measurements and HOD/HMQ comparisons rest on independent simulations and priors, with only minor non-load-bearing self-citation.

full rationale

The paper's central claims compare field-level EFT parameters measured from the hydrodynamic MTNG and Astrid simulations against EFT parameter distributions generated from AbacusSummit N-body mocks populated with HOD/HMQ prescriptions. The hydro measurements are obtained by fitting transfer functions of the field-level EFT model (Section 3.4 and Eqs. 17-24) directly to the simulated galaxy density fields, with no HOD/HMQ parameters fitted to those fields. The HOD priors come from previous work by the same group (refs. [35,36]), but these are independent mock catalogs with parameter priors taken from refs. [109,80], not calibrations to MTNG/Astrid data; the HMQ ELG catalogs are generated in this paper from DESI-motivated priors. The neural-density-estimation section (Section 4.4) trains a normalizing flow on paired HOD-EFT samples from [35,36] and then applies it to the independently measured hydro EFT parameters; this is an inverse mapping from measurements to HOD parameters, not a prediction forced by construction. The analytic b2 argument (Section 4.3, Eqs. 25-29) uses the measured halo-occupation weighting of the hydro galaxies to explain the measured b2 values, which is a consistency check rather than an input-defined result. The only mild self-referential element is that the EFT parameter extraction pipeline is shared between the HOD mocks and the hydro galaxies, and that the LRG-HOD baseline priors stem from the same group's earlier papers; however, the hydro galaxy fields are external benchmarks entering no fit, so this does not make the comparison circular. A redshift mismatch between the LRG-HOD baseline (z=0.5) and the hydro ELG samples (z=1) is a potential validity concern for the ELG-vs-LRG-HOD tension claim, but it is an astrophysical/statistical robustness issue, not a circularity pattern. Overall, the derivation chain is self-contained against external simulations and no fitted parameter is renamed as a prediction.

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

The paper does not introduce new entities. Its central comparison rests on standard EFT and HOD priors from the authors' prior work. The chosen scale cuts (kmax, kS) are free choices that affect the measured parameter values but not the qualitative conclusions. The main load-bearing assumptions are the galaxy selection proxy and the validity of the EFT model at the quoted scale cuts.

free parameters (3)
  • kmax (scale cuts for EFT fits) = 0.4 and 0.2 h/Mpc (MTNG), 0.4 h/Mpc (Astrid redshift space)
    Chosen to stay within the perturbative regime; different values would change the measured EFT parameters and hence the comparison, though standard in the field.
  • kS in stochastic noise model = 0.45 h/Mpc
    Reference scale in the error power spectrum model, chosen following ref [28]; affects the stochastic parameter fits.
  • HMQ quenching efficiency Q = 100
    Fixed in the HMQ model following ref [113]; not varied, so the ELG prior depends on this external choice.
assumptions (4)
  • domain assumption The EFT bias expansion through cubic order plus the stochastic noise model (eqs. 17-24) accurately describes the galaxy density field on quasi-linear scales.
    Assumed from the EFT of large-scale structure literature; used throughout Section 3.4 and tested via the cross-correlation coefficient in Fig. 6.
  • domain assumption The sSFR cut at fixed number density selects galaxy samples equivalent to BOSS LRGs and DESI ELGs for the purpose of comparing EFT parameters.
    Following refs [62-65]; the paper notes that color modeling gives similar results, but this equivalence is load-bearing for transferring conclusions to survey samples.
  • domain assumption The HOD and HMQ parameter priors from refs [35,36,80] span the plausible range of galaxy-halo connection models.
    The comparison and the NF-based mapping treat these priors as the relevant model space; the paper does not test the sensitivity to the prior bounds.
  • standard math Mass function and bias relations for the analytic b2 argument follow the Press-Schechter model with dn/dM proportional to M^-n (n approximately 2).
    Used in Section 4.3 to derive the enhancement of galaxy b2 over halo b2; an approximation that ignores satellites.

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Cite this review

Pith. "Pith review of The Millennium and Astrid galaxies in effective field theory: comparison with galaxy-halo connection models at the field level." pith.science (2026). https://pith.science/paper/IAASVOE6

@misc{pith2026241201888,
  author       = {Pith},
  title        = {Pith review of: The Millennium and Astrid galaxies in effective field theory: comparison with galaxy-halo connection models at the field level},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IAASVOE6}},
  note         = {Machine review of arXiv:2412.01888}
}
read the original abstract

Cosmological analyses of redshift space clustering data are primarily based on using luminous ``red'' galaxies (LRGs) and ``blue'' emission line galaxies (ELGs) to trace underlying dark matter. Using the large high-fidelity high-resolution MillenniumTNG (MTNG) and Astrid simulations, we study these galaxies with the effective field theory (EFT)-based field level forward model. We confirm that both red and blue galaxies can be accurately modeled with EFT at the field level and their parameters match those of the phenomenological halo-based models. Specifically, we consider the state of the art Halo Occupation Distribution (HOD) and High Mass Quenched (HMQ) models for the red and blue galaxies, respectively. Our results explicitly confirm the validity of the halo-based models on large scales beyond the two-point statistics. In addition, we validate the field-level HOD/HMQ-based priors for EFT full-shape analysis. We find that the local bias parameters of the ELGs are in tension with the predictions of the LRG-like HOD models and present a simple analytic argument explaining this phenomenology. We also confirm that ELGs exhibit weaker non-linear redshift-space distortions (``fingers-of-God''), suggesting that a significant fraction of their data should be perturbative. We find that the response of EFT parameters to galaxy selection is sensitive to assumptions about baryonic feedback, suggesting that a detailed understanding of feedback processes is necessary for robust predictions of EFT parameters. Finally, using neural density estimation based on paired HOD-EFT parameter samples, we obtain optimal HOD models that reproduce the clustering of Astrid and MTNG galaxies.

Figures

Figures reproduced from arXiv: 2412.01888 by the authors.

Figure 1
Figure 1. FIG. 1. MTNG and Astrid bias parameters for LRGs against the LRG-HOD-based density distribution (LRG-HOD priors). [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. MTNG and ASTRID bias parameters of ELGs vs. the distributions extracted from LRG-based HOD and ELG-based [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The samples of MTNG and Astrid galaxies in the stellar mass - specific star formation rate planes. We display blue [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The MTNG DESI-like LRG density field in real space (upper panel) and in redshift space (lower panel) from the [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. EFT model transfer functions and noise power spectra for MTNG galaxies in real space (black lines) and in redshift [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Cross-correlation coefficients [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. MTNG and Astrid redshift-space counterterms for LRGs and ELGs vs the LRG-HOD priors. [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. MTNG and Astrid real space EFT parameters of LRGs against two LRG-HOD-based distributions: LRG-HOD-I [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Same as fig [PITH_FULL_IMAGE:figures/full_fig_p016_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. MTNG and Astrid redshift-space counterterms for ELGs vs the LRG-HOD and ELG-HMQ based distributions. [PITH_FULL_IMAGE:figures/full_fig_p018_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Quadratic bias parameters [PITH_FULL_IMAGE:figures/full_fig_p019_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. The mass function of halos hosting the hydrodynamic galaxies, i.e. [PITH_FULL_IMAGE:figures/full_fig_p019_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13. Inferred distribution of LRG-HOD parameters for MTNG as translated with our learned conditional distribution and [PITH_FULL_IMAGE:figures/full_fig_p021_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14. Same as fig [PITH_FULL_IMAGE:figures/full_fig_p022_14.png]
Figure 15
Figure 15. Figure 15: FIG. 15. Inferred distribution of HOD parameters for MTNG ELGs as translated with our learned conditional distribution and [PITH_FULL_IMAGE:figures/full_fig_p023_15.png]
Figure 16
Figure 16. Figure 16: FIG. 16. Same as fig [PITH_FULL_IMAGE:figures/full_fig_p024_16.png]

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Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.