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arxiv: 2606.12565 · v1 · pith:FZJ4LQSNnew · submitted 2026-06-10 · 🌌 astro-ph.CO · astro-ph.GA

Galaxy formation in modified gravity -- II. galaxy halo connection and assembly bias

Michael Collier , Sownak Bose , Baojiu Li This is my paper

Pith reviewed 2026-06-27 08:21 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GA
keywords modified gravityhalo occupation distributionassembly biasgalaxy clusteringf(R) gravitychameleon screeninglarge-scale structureemission line galaxies
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The pith

Adding environment density to the halo occupation model reduces assembly bias effects to 2-3% at low redshifts in both standard and modified gravity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that the standard halo occupation distribution, which ties galaxies only to halo mass, underestimates clustering strength because it ignores assembly bias. In modified gravity simulations this mismatch grows more involved due to chameleon screening, yet a simple physical trend appears where more massive halos form galaxies more readily over time. Extending the model with environment density as a secondary variable brings the assembly bias residual down to 2-3% for redshifts below 0.5 across all cosmologies tested. This matters because upcoming surveys need reliable galaxy-halo links to extract cosmological information from large-scale structure.

Core claim

While the basic halo occupation distribution underestimates galaxy clustering by 10-20% in Lambda CDM when assembly bias is neglected, and introduces further complexity in f(R) gravity, extending the model with a suitably chosen environment density as a secondary HOD variable reduces the assembly bias effect in all models to 2-3% for z less than or equal to 0.5. The simulations show halo and galaxy formation enhanced for progressively more massive haloes over time under chameleon screening.

What carries the argument

the halo occupation distribution extended by environment density as a secondary variable to capture assembly bias

If this is right

  • Standard mass-only HOD models underestimate clustering strength by 10-20% at z less than or equal to 1 when assembly bias is ignored.
  • Modified gravity adds extra complexity to the galaxy-halo connection through the chameleon screening mechanism.
  • Environment density as a secondary variable reduces the assembly bias residual to 2-3% for z less than or equal to 0.5 in every model examined.
  • The adjusted model supplies a practical starting point for controlling assembly bias when testing non-standard cosmologies with large-scale structure surveys.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Survey analyses could adopt this secondary variable to obtain tighter limits on f(R) parameters from clustering measurements.
  • Alternative environmental measures might be tested in the same simulations to see if the residual can be lowered further.
  • The approach may generalise to other modified gravity scenarios where screening also depends on local density.

Load-bearing premise

The mock emission line galaxy and luminous red galaxy catalogues generated from the modified gravity hydrodynamical simulations accurately capture the effects of chameleon screening on galaxy and halo formation.

What would settle it

A direct measurement of the two-point clustering amplitude of emission line or luminous red galaxies in DESI or Euclid data at z less than or equal to 0.5 compared against the prediction from the environment-density HOD model; a deviation larger than a few percent would show the claimed reduction does not hold.

Figures

Figures reproduced from arXiv: 2606.12565 by Baojiu Li, Michael Collier, Sownak Bose.

Figure 1
Figure 1. Figure 1: The leftmost panel shows the median sSFR in bins of stellar mass for our GR simulation and for TNG300. The central and rightmost panels show the sSFR and stellar masses plotted for subhaloes in both our GR run and TNG300. Blue points show objects corresponding to cuts M⋆ > 3 × 1011 M⊙ and sSFR > 10−9.5 yr−1 . ELG LRG z log10(sSFR [yr−1 ]) M⋆ [1010 M⊙] 1.16 −9.3 7.5 0.97 −9.4 7.4 0.73 −9.5 8.2 0.51 −9.6 8.2… view at source ↗
Figure 2
Figure 2. Figure 2: A demonstration of the effect of varying the different HOD parameters on the central ELG mean occupancy. The black curve corresponds to parameter values (σM, γ, Q, pmax, log Mc) = (0.2, 2.0, 30.0, 0.11, 12.0), i.e., the lowest value in the range of variation of each parameter in this figure. The shaded regions show the space swept out by gradually increasing the value of each parameter over the range shown… view at source ↗
Figure 3
Figure 3. Figure 3: Upper row: Mean occupations of ELG-hosting haloes as a function of M200,c. Different line styles show the total, central and satellite occupations as indicated by the legend in the rightmost subpanel. The shaded region shows the standard error on the mean total occupation for GR, inflated by a factor of 5 to aid visibility. The smaller subpanels show the relative difference between each MG model and GR. Lo… view at source ↗
Figure 4
Figure 4. Figure 4: Best-fit ELG HOD parameters as a function of redshift. The HODs correspond to galaxy populations with a fixed number density of 0.001 h 3Mpc−3 . The solid curves show the best-fit parameters smoothed over redshift using Gaussian smoothing with σ = 1.5 plotted points. The unsmoothed curves are shown underneath as faded curves of the same colour. mean occupancy value at this peak. In GR, both parameters decr… view at source ↗
Figure 5
Figure 5. Figure 5: Best-fit LRG HOD parameters as a function of redshift. The HODs correspond to galaxy populations with a fixed number density of 0.001 h 3Mpc−3 . The solid curves show the best-fit parameters smoothed over redshift using Gaussian smoothing with σ = 1.5 plotted points. The unsmoothed curves are shown underneath as faded curves of the same colour. enhanced the growth of both haloes and the LRGs they host, kee… view at source ↗
Figure 6
Figure 6. Figure 6: HOD parameters for ELG samples at ng = 0.001 h 3Mpc−3 , divided into 4 subsamples corresponding to galaxies hosted by haloes in a particular quartile of environment density. Each row corresponds to one parameter, and each column corresponds to parameter values of one gravity model, with line styles indicating different quartiles of environment. To improve visibility, solid curves show the fitted parameters… view at source ↗
Figure 7
Figure 7. Figure 7: HOD parameters for LRG samples at ng = 0.001 h 3Mpc−3 , divided into 4 subsamples corresponding to galaxies hosted by haloes in a particular quartile of environment density. Each row corresponds to one parameter, and each column corresponds to parameter values of one gravity model, with line styles indicating different quartiles of environment. To improve visibility, solid curves show the fitted parameters… view at source ↗
Figure 8
Figure 8. Figure 8: HOD parameters for ELG samples at ng = 0.001 h 3Mpc−3 , divided into 4 subsamples corresponding to galaxies hosted by haloes in a particular quartile of concentration. Each row corresponds to one parameter, and each column corresponds to fitted parameter values of one gravity model, with line styles indicating different quartiles of concentration. To improve visibility, solid curves show the parameters smo… view at source ↗
Figure 9
Figure 9. Figure 9: HOD parameters for LRG samples at ng = 0.001 h 3Mpc−3 , divided into 4 subsamples corresponding to galaxies hosted by haloes in a particular quartile of concentration. Each row corresponds to one parameter, and each column corresponds to fitted parameter values of one gravity model, with line styles indicating different quartiles of concentration. To improve visibility, solid curves show the parameters smo… view at source ↗
Figure 10
Figure 10. Figure 10: The averaged large-scale correlation function (defined in the main text) of ELG (top row) and LRG (bottom row) galaxy samples generated, from left to right panels, by: (i) using the measured basic HOD to populate haloes, (ii) using the measured HOD in environment percentiles to populate haloes, and (iii) using measured HOD in concentration percentiles to populate haloes. We show the relative difference be… view at source ↗
read the original abstract

Modern surveys such as DESI and \textit{Euclid}, which collect data for hundreds of millions of galaxies to map the large-scale structure (LSS) of the Universe, hold the key to determining the cosmological parameters and testing new physics. This ambition, however, is limited by uncertainties in the galaxy-halo connection: the link between observed galaxies and the underlying, unobservable matter field, by accounting for effects such as galaxy bias and assembly bias (AB). These are particularly poorly-understood for modified gravity (MG) models, which are popular alternatives to the cosmological constant to explain accelerated expansion. We approach this problem using mock emission line galaxy (ELG) and luminous red galaxy (LRG) catalogues in $f(R)$ gravity matching the specifications of ongoing Stage-IV galaxy surveys, generated from state-of-the-art MG hydrodynamical simulations. While the interplay between MG -- especially the chameleon screening mechanism -- and galaxy formation leaves complicated imprints in the galaxy-halo connection, a simple physical picture emerges in which halo and galaxy formation are enhanced for progressively more massive haloes over time. We confirm that the basic galaxy-halo connection model, the halo occupation distribution (HOD), in which galaxy occupation is determined solely by halo mass, underestimates galaxy clustering strength in $\Lambda$CDM by $10$--$20\%$ at $z\lesssim1$ when neglecting AB, and demonstrate that MG introduces further complexity. Extending this model with a suitably-chosen environment density as a secondary HOD variable reduces the AB effect in all models to $2$--$3\%$ for $z\lesssim0.5$. This provides a well-motivated starting point for further works on minimising the impact of AB when testing non-standard cosmological models with LSS.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper uses state-of-the-art f(R) hydrodynamical simulations to generate mock ELG and LRG catalogs matching Stage-IV survey specifications. It examines the galaxy-halo connection via HOD modeling, shows that standard mass-only HOD underestimates clustering by 10-20% at z≲1 due to assembly bias (AB), and demonstrates that adding a suitably chosen environment density as a secondary HOD variable reduces the AB effect to 2-3% for z≲0.5 across ΛCDM and MG models.

Significance. If the mocks accurately capture chameleon screening, the result supplies a concrete, low-parameter extension to HOD modeling that mitigates AB contamination when testing gravity with upcoming LSS data. This is a practical advance for cosmological analyses in non-standard gravity.

major comments (2)
  1. [Sections 3 and 4] Sections 3 and 4: The central claim that environment density reduces AB to 2--3% at z≲0.5 in all models rests on the mocks faithfully encoding how chameleon screening modulates halo assembly and galaxy occupation. No quantitative isolation of the MG imprint is shown (e.g., direct comparison of screened vs. unscreened runs, resolution study of the scalar-field solver, or test against analytic screening thresholds), so it is unclear whether the measured reduction is robust or an artifact of the particular sub-grid galaxy model and numerical setup.
  2. [Abstract and results sections] Abstract and results sections: The reported 10--20% underestimation and 2--3% residual AB values are given without error bars, sample-variance estimates, or resolution-convergence tests. Because the headline percentages are load-bearing for the practical utility claim, the absence of these quantifications prevents assessment of whether the reduction is statistically significant or simulation-specific.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. The comments identify important areas where additional quantification and explicit tests can strengthen the robustness of our results on assembly bias mitigation in f(R) gravity. We address each major comment below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Sections 3 and 4] Sections 3 and 4: The central claim that environment density reduces AB to 2--3% at z≲0.5 in all models rests on the mocks faithfully encoding how chameleon screening modulates halo assembly and galaxy occupation. No quantitative isolation of the MG imprint is shown (e.g., direct comparison of screened vs. unscreened runs, resolution study of the scalar-field solver, or test against analytic screening thresholds), so it is unclear whether the measured reduction is robust or an artifact of the particular sub-grid galaxy model and numerical setup.

    Authors: The hydrodynamical simulations used here solve the scalar-field equation to capture chameleon screening self-consistently, as detailed in Section 2 and validated against analytic thresholds in the simulation methodology papers and our companion Paper I. We acknowledge that an explicit isolation of the MG contribution would strengthen the presentation. In the revision we will add a direct comparison of halo assembly bias and galaxy occupation between the f(R) and ΛCDM runs (new panel or subsection in Section 3) to quantify the additional MG imprint. We will also cite the existing resolution and convergence tests for the scalar-field solver performed during simulation development. A new dedicated resolution study lies outside the scope of the present work but the cited tests address the concern that the reported reduction is an artifact. revision: partial

  2. Referee: [Abstract and results sections] Abstract and results sections: The reported 10--20% underestimation and 2--3% residual AB values are given without error bars, sample-variance estimates, or resolution-convergence tests. Because the headline percentages are load-bearing for the practical utility claim, the absence of these quantifications prevents assessment of whether the reduction is statistically significant or simulation-specific.

    Authors: We agree that error bars and sample-variance estimates are necessary to support the headline percentages. In the revised manuscript we will add jackknife resampling errors (over the simulation volume) to the clustering ratios and AB reduction values reported in the abstract and Sections 3–4. We will also include a short paragraph referencing the resolution convergence tests already performed for the underlying simulation suite. These additions will allow quantitative assessment of statistical significance. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results from direct simulation outputs and empirical HOD fits

full rationale

The paper derives its claims about galaxy-halo connection, assembly bias, and the effect of adding environment density as a secondary HOD variable directly from outputs of MG hydrodynamical simulations and subsequent fitting to mock ELG/LRGs catalogs. No equations or steps reduce a claimed prediction to a fitted input by construction, nor do any load-bearing premises rely on self-citations whose content is unverified or equivalent to the target result. The derivation chain is self-contained against external benchmarks (the simulations themselves) with no renaming of known results or smuggling of ansatzes via citation.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The study depends on assumptions from modified gravity theory and simulation methods whose details are not provided in the abstract.

free parameters (1)
  • HOD environment density threshold
    Chosen to minimize AB effect, likely tuned to simulation outputs.
axioms (1)
  • domain assumption Chameleon screening mechanism operates as modeled in f(R) gravity simulations
    Invoked to explain enhanced formation in massive haloes.

pith-pipeline@v0.9.1-grok · 5864 in / 1192 out tokens · 24400 ms · 2026-06-27T08:21:02.669909+00:00 · methodology

discussion (0)

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Reference graph

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