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arxiv: 2604.21790 · v1 · submitted 2026-04-23 · 🌌 astro-ph.CO

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Informative Priors on Primordial Non-Gaussianity Bias b_{φ} From Galaxy Formation

Anne Moore , Lucia A. Perez , Elisabeth Krause
Authors on Pith no claims yet

Pith reviewed 2026-05-08 14:01 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords primordial non-Gaussianitygalaxy biasstellar mass functionstellar-to-halo mass relationcosmological simulationsf_NLDESI ELGseparate universe simulations
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The pith

Conditioning on stellar mass function and halo mass relation reduces uncertainty in b_φ by up to 97 percent

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

The paper develops a method to build observation-based priors for the galaxy bias parameter b_φ that is degenerate with the primordial non-Gaussianity amplitude f_NL at leading order. Using simulations that vary galaxy formation physics, the authors measure how b_φ changes across different stellar mass functions and stellar-to-halo mass relations for a sample resembling DESI emission-line galaxies. They then construct conditional distributions of b_φ given these observables and show that the spread narrows sharply. This tightening occurs because the chosen observables strongly correlate with the response that sets b_φ. The resulting priors are tight enough that galaxy-formation uncertainty no longer dominates constraints on f_NL from next-generation spectroscopic surveys.

Core claim

We present a framework to construct physically motivated, observation-conditioned priors on b_φ by marginalizing over galaxy formation uncertainties. We use the CAMELS-SAM simulation suite, augmented by separate Universe simulations, to measure galaxy formation observables like the stellar mass function and the stellar-to-halo mass relationship, and b_φ across a range of galaxy formation parameters. From these measurements we construct a distribution of b_φ conditioned on observations for a DESI ELG-like sample. Conditioning on the SMF or SHMR decreases σ_bφ from 0.69 to 0.08 and 0.02 respectively, reductions of 88 percent and 97 percent, with consistent results when conditioning on the data

What carries the argument

A simulation-based framework that measures b_φ response across galaxy-formation parameter variations and builds conditional priors on the stellar mass function and stellar-to-halo mass relation for a chosen galaxy population

If this is right

  • The uncertainty on b_φ falls from 0.69 to 0.08 when the prior is conditioned on the stellar mass function
  • Conditioning on the stellar-to-halo mass relation reduces the same uncertainty further to 0.02
  • The tightened priors remain consistent even after accounting for known discrepancies between the simulations and real data at high halo masses
  • The stellar mass function and stellar-to-halo mass relation together supply enough information to keep galaxy-formation uncertainty from limiting f_NL constraints in next-generation surveys

Where Pith is reading between the lines

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

  • The same conditioning technique could be applied to other bias parameters or to additional observables such as galaxy clustering statistics themselves
  • If real galaxy formation includes processes outside the varied parameters of the CAMELS-SAM suite, the actual reduction in b_φ uncertainty would be smaller than reported
  • Extending the method to include direct clustering data in the conditioning step could further tighten the priors without relying on external mass-function measurements

Load-bearing premise

The chosen set of galaxy-formation parameter variations in the CAMELS-SAM suite and the separate-universe measurements together span the full range of relevant uncertainties in b_φ without missing important physics or adding unaccounted systematics

What would settle it

A future measurement of b_φ from DESI-scale clustering data that lies well outside the conditional distributions predicted after marginalizing over the SMF or SHMR would show that the priors do not capture the true uncertainty

read the original abstract

Constraining primordial non-Gaussianity via its scale-dependent imprint on galaxy clustering requires knowledge of the bias parameter $b_{\phi}$, which is exactly degenerate with $f^{\rm{loc}}_{\rm{NL}}$ at leading order. To break this degeneracy, current analyses adopt the relation $\left(b_{\phi} = 2\delta_c\left(b_1 - 1\right)\right)$ based on the assumption of a universal mass function. This relation is known to break down for physically motivated galaxy selections, introducing systematic errors in the inferred $f^{\rm{loc}}_{\rm{NL}}$ that scale directly with the assumed $b_{\phi}$ prior. We present a framework to construct physically motivated, observation-conditioned priors on $b_{\phi}$ by marginalizing over galaxy formation uncertainties. We use the CAMELS-SAM simulation suite, augmented by separate Universe simulations, to measure galaxy formation observables, like the stellar mass function (SMF) and the stellar-to-halo mass relationship (SHMR), and $b_{\phi}$ across a range of galaxy formation parameters. From these measurements, we construct a distribution of $b_{\phi}$ conditioned on observations, and we select our galaxy sample to resemble the DESI Emission Line Galaxy (ELG) sample. Conditioning on the SMF or SHMR decreases $\sigma_{b_{\phi}}$ from $0.69$ to $0.08$ and $0.02$ respectively -- reductions of $88\%$ and $97\%$ -- with consistent results when conditioning on the observed data directly. Despite substantial shifts in the galaxy formation posteriors driven by known SC-SAM discrepancies at high halo masses, the resulting $b_{\phi}$ distributions remain mutually consistent across all observables. The SMF and SHMR are found to carry sufficient constraining power to reduce the galaxy formation uncertainty in $b_{\phi}$ relevant for $f^{\rm{loc}}_{\rm{NL}}$ inference with next-generation spectroscopic surveys

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 / 2 minor

Summary. The paper presents a framework for constructing observationally conditioned priors on the galaxy bias parameter b_φ (which is degenerate with f_NL^loc) by marginalizing over galaxy formation uncertainties in the CAMELS-SAM suite. Separate-universe simulations are used to measure b_φ alongside the stellar mass function (SMF) and stellar-to-halo mass relation (SHMR) for a DESI-like ELG sample; conditioning on these observables is reported to reduce σ_bφ from 0.69 to 0.08 (SMF) and 0.02 (SHMR), with consistent results when conditioning directly on observed data.

Significance. If the CAMELS-SAM parameter variations and separate-universe measurements adequately capture the relevant uncertainties, the method could supply tighter, physically motivated priors that reduce systematic errors in f_NL^loc inference for next-generation surveys. The reported consistency of b_φ distributions despite shifts in galaxy-formation posteriors is a positive indication of robustness, but the quantitative reductions depend on the completeness of the simulation suite.

major comments (2)
  1. The headline reductions in σ_bφ (Abstract) rest on the assumption that the chosen CAMELS-SAM galaxy-formation parameter variations span all relevant uncertainties in the b_φ response for the selected ELG population. The manuscript notes known SC-SAM discrepancies at high halo masses yet reports mutually consistent b_φ distributions; however, it does not demonstrate that unvaried physics (e.g., alternative feedback implementations, assembly bias, or baryonic effects outside the SAM) would not produce additional scatter that survives SMF/SHMR conditioning.
  2. Details on the extraction of b_φ from the separate-universe runs, including how the response is measured for the selected galaxy population and any validation against other codes or analytic expectations, are not provided. This information is load-bearing for interpreting the reported σ_bφ values and their reduction factors.
minor comments (2)
  1. Clarify the precise definition and measurement procedure for b_φ in the separate-universe simulations (e.g., which halo/galaxy properties are used and how selection effects are handled).
  2. Provide quantitative cross-checks (e.g., tables or figures) showing the b_φ distributions before and after conditioning, including the impact of the high-mass discrepancies on the final priors.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their constructive and detailed report. The comments identify important areas for clarification and additional discussion. We address each major comment below and will revise the manuscript accordingly to improve transparency and acknowledge limitations.

read point-by-point responses

  1. Referee: The headline reductions in σ_bφ (Abstract) rest on the assumption that the chosen CAMELS-SAM galaxy-formation parameter variations span all relevant uncertainties in the b_φ response for the selected ELG population. The manuscript notes known SC-SAM discrepancies at high halo masses yet reports mutually consistent b_φ distributions; however, it does not demonstrate that unvaried physics (e.g., alternative feedback implementations, assembly bias, or baryonic effects outside the SAM) would not produce additional scatter that survives SMF/SHMR conditioning.

    Authors: We agree that the CAMELS-SAM parameter variations, while spanning key processes in the SC-SAM framework, do not exhaust all possible galaxy formation uncertainties. The reported consistency of the b_φ distributions across shifted galaxy-formation posteriors (driven by the high-mass SC-SAM discrepancies) indicates that the SMF and SHMR conditioning captures the dominant variations relevant to b_φ within this suite. However, we acknowledge that unvaried aspects such as alternative feedback implementations or explicit assembly bias could introduce additional scatter. In the revised manuscript we will expand the discussion to explicitly state this limitation and its implications for the generality of the priors. revision: partial

  2. Referee: Details on the extraction of b_φ from the separate-universe runs, including how the response is measured for the selected galaxy population and any validation against other codes or analytic expectations, are not provided. This information is load-bearing for interpreting the reported σ_bφ values and their reduction factors.

    Authors: We thank the referee for noting this omission. b_φ is extracted via the standard separate-universe response: the fractional change in the number density of the ELG-selected galaxies between the fiducial and δ_L = ±0.1 runs, divided by the long-mode amplitude. The ELG sample is defined by stellar-mass and specific star-formation-rate cuts chosen to reproduce DESI ELG properties. We will add a dedicated methods subsection with the exact measurement formula, selection criteria, and uncertainty estimation. We will also include a validation comparison of the halo-level response against the analytic peak-background-split expectation, together with references to prior literature using analogous techniques. These additions will appear in the revised manuscript. revision: yes

standing simulated objections not resolved
  • We cannot demonstrate that physics not varied within the CAMELS-SAM suite (e.g., entirely different feedback or hydrodynamical implementations) would produce no additional scatter after SMF/SHMR conditioning, as this would require simulation suites beyond the scope of the present work.

Circularity Check

0 steps flagged

No significant circularity: b_φ measured directly from separate-universe simulations and conditioned on independent observables

full rationale

The paper's core derivation measures b_φ directly from separate-universe simulations run across CAMELS-SAM galaxy-formation parameter variations, then constructs a posterior distribution for b_φ by conditioning on the independently measured SMF and SHMR (or observed data). This process does not reduce by construction to a fitted parameter, self-defined relation, or self-citation chain; the quoted reductions in σ_bφ (0.69 → 0.08/0.02) arise from the simulation-based marginalization over galaxy-formation uncertainties rather than from any equation that equates the output to its inputs. No load-bearing step invokes a uniqueness theorem, ansatz smuggled via prior work, or renaming of a known result. The framework remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the CAMELS-SAM suite spanning relevant galaxy formation uncertainties and on the separate-universe technique providing an accurate b_φ measurement; no new entities are postulated.

axioms (2)
  • domain assumption The CAMELS-SAM simulation suite with its parameter variations adequately spans the relevant uncertainties in b_φ for the purpose of marginalization
    Invoked when constructing the prior distribution from the simulation measurements.
  • domain assumption Separate-universe simulations correctly capture the linear response of galaxy number density to long-wavelength modes for the chosen galaxy selection
    Used to measure b_φ across the range of galaxy formation parameters.

pith-pipeline@v0.9.0 · 5672 in / 1669 out tokens · 61945 ms · 2026-05-08T14:01:42.225918+00:00 · methodology

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Reference graph

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