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Stress-Testing Small-Scale Cosmological Inference With Empirical Galaxy--Halo Connection Models

Hanyue Wang, Kate Storey-Fisher, Philip Mansfield, Andrew Hearin, Marcelo Alvarez, Suchetha Cooray, Risa H. Wechsler

Nov 3, 2026arXiv:2611.04419v1
astro-ph.CO
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Scorecard· 16/16
6.5/10 impact

Timely, well-executed closure test showing HOD-based small-scale inference can be biased while SHAM recovers S8, but limited by a single, SHAM-like target and a coarse CEM emulation.

Abstract

Small-scale galaxy clustering contains substantial cosmological information, but extracting it reliably requires robust modeling of the galaxy--halo connection. In this work, we compare two widely adopted families of empirical models, subhalo abundance matching (SHAM) and the halo occupation distribution (HOD), testing their predictions for galaxy clustering and their recovery of the input cosmology. Using Aemulus-ββ, a new multi-cosmology simulation suite with substructure merger trees, we fit multiple SHAM and HOD models to the small-scale clustering of a stellar-mass-selected mock galaxy catalog generated with the more physical semi-empirical model UniverseMachine. We then use cosmological evidence modeling to infer the structure growth parameter S8S_8. Our results show that the SHAM model, regardless of the treatment of numerically disrupted subhalos, is able to offer tight, unbiased constraints on S8S_8 with ~2-3% precision, using simulations of relatively small volumes that span a limited number of cosmologies. In contrast, HOD models, even when accounting for assembly bias, yield weaker and potentially biased cosmological constraints that are sensitive to implementation choices: the inferred S8S_8 degrades in precision to ~6-11% and can be offset by ~1σσ. This suggests that the excessive parametric flexibility and model misspecification of most commonly adopted HOD models can degrade and bias the resulting cosmological constraints. We further evaluate each model's performance in predicting higher-order statistics not used in the fit and find that SHAM generally reproduces them more accurately than the tested HOD models. These results highlight the potential of leveraging predictive subhalo-level information from simulations to enable robust cosmological inference on small scales.

AI Impact Assessments

(1 model)

Core Contribution

The paper stress-tests two standard empirical galaxy–halo connection frameworks, SHAM and HOD, for small-scale cosmological inference. The target is a UniverseMachine mock (log M* ≥ 10.5) built on the new Aemulus-β multi-cosmology suite. That suite has 25 wCDM boxes (22 usable), 2048³ particles in 400 h⁻¹Mpc, and merger trees. The authors fit w_p down to 0.5 Mpc at each cosmology and use Cosmological Evidence Modeling (CEM) to build an S8 posterior from the nested-sampling evidences. The main findings:

  • A new two-parameter SHAM (interpolating halo proxies via the epoch of peak mass, with and without orphans) yields unbiased S8 at ~2–3% precision.
  • Vanilla HOD is strongly biased. Four assembly-bias-extended HODs (dHOD and AbacusHOD, with concentration or environment as the secondary property) give ~6–11% precision with ~1σ upward offsets.
  • SHAM better predicts counts-in-cylinders and multiplet clustering, which were not used in the fit.

    • The conceptual message is that a good fit to w_p at fixed cosmology does not imply unbiased cosmology. HOD flexibility plus misspecified assembly bias lets models absorb cosmology-dependent signal. The paper also extends CEM to subhalo-based models for the first time.

    Methodological Rigor

    Strengths:

  • The test is a proper end-to-end closure test with a known truth.
  • Fits at the true cosmology are separated from cosmology recovery.
  • The covariance comes from a large MDPL2 jackknife with the Mohammad & Percival correction, rescaled by volume.
  • The evidence-vs-S8 curves are shown.
  • Appendix B tests SHAM self-recovery.
  • Posterior predictive checks and the orphan sensitivity analysis are useful.
  • The authors are candid about limitations.

    • Weaknesses:

  • Only one target model and one cosmology are used. UniverseMachine shares a subhalo-level, assembly-history philosophy with SHAM, so SHAM's success is partly circular. The authors acknowledge this, but it substantially weakens the headline "SHAM is robust" claim. A fairer reading is that SHAM works when the truth is subhalo-based.
  • The target and models share the same simulation box, so cosmic variance is identical. The χ² values are implausibly low, which means the test is optimistic.
  • CEM relies on a 1D Gaussian in S8 fit to ~21 evidence points. The tested alternatives (skew-normal, 2D Gaussian) are only briefly described. Posterior widths of 1.5–3% from 21 noisy points, and the difference between 0.015 and 0.028 for the two SHAM variants, carry real uncertainty from the fit. The "unbiased" claim rests on a single realization. The 1σ HOD offsets are marginal for individual models, since only one target and one noise realization exist.
  • The 3 h⁻¹Mpc environment scale was chosen by fit quality. The HOD variants tested are limited; they exclude, for example, velocity bias, more flexible secondary-property forms, and multiple secondary properties combined.
  • The data vector is minimal (w_p only, no RSD, no real survey effects). The CiC covariance is admitted to be unreliable, so the higher-order statistic comparison is qualitative.
  • Using the HOD's "excess flexibility" as an explanation is plausible but not isolated by ablation. Misspecification and flexibility are conflated.
  • The bias is also driven by a single 1D parameter, and the other cosmological parameters were not explored.

    • Potential Impact

    The paper is directly relevant to DESI BGS/BGS-like small-scale analyses, Euclid, and Roman. It offers a cautionary, concrete demonstration that HOD-based small-scale inference can be biased even when fits look good. It also offers a practical alternative that works with few high-resolution simulations, avoiding emulation or rescaling errors. The Aemulus-β suite and the SHAM parameterization are reusable assets, although the suite is "in prep". The assembly bias analysis in UniverseMachine (concentration vs. environment, central vs. satellite, splashback contamination) is informative for HOD practitioners. The finding that environment-based assembly bias degrades S8 constraints because of degeneracy is a useful caution, since it improves fits to real data. Realistically, though, adoption by the community depends on validation against hydrodynamic or semi-analytic truths and on real data. The community may also see the result as specific to a test where the target resembles SHAM.

    Timeliness & Relevance

    The timing is excellent. Small-scale clustering and simulation-based inference are central to the DESI era. Model misspecification and the galaxy–halo connection are widely recognized as the main systematic. The paper also fits the growing trend of "stress tests" with multiple galaxy formation models.

    Strengths

  • Clear, well-posed question with an unambiguous truth.
  • First use of CEM with subhalo-based models, built directly on high-resolution simulations across cosmologies.
  • Careful treatment of orphans, assembly bias diagnostics, and honest discussion of caveats.
  • Predictive tests on non-fitted statistics add independent evidence.

    • Limitations

  • Single mock, a target structurally close to SHAM, and a single realization.
  • Small simulation volume and few cosmologies, with a Gaussian-in-S8 ansatz.
  • The HOD comparison covers a limited set of variants, and the HOD "failure" may be specific to those implementations.
  • No real-data application; code and data availability are unclear (Aemulus-β is not yet published).
  • Only S8 is constrained, with no multi-parameter inference.

    • Overall

    This is a solid, timely, moderately influential methodology and validation paper. It is unlikely to be paradigm-shifting, but it will be cited in small-scale clustering and galaxy–halo connection analyses, and it raises important questions about HOD reliability. The conclusions would be stronger with a more independent target.

    Rating:6.5/ 10
    Significance 6.5Rigor 6Novelty 6Clarity 7

    Generated Nov 4, 2026

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