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REVIEW 3 major objections 5 minor 132 references

Disentangling modified gravity and galaxy bias with field-level inference

T0 review · 3 major / 5 minor · reviewed 2026-07-12 · grok-4.5

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Pith's one-line read Field-level analysis of the full galaxy map breaks the modified-gravity/bias degeneracy that power spectra cannot resolve.

desk verdict Clean controlled demo that field-level Poisson on n_g breaks the f(R)–β degeneracy under known phases; the idealisation is already their stated limit. read the letter →

arxiv 2607.03514 v1 pith:UGCNLM57 submitted 2026-07-03 astro-ph.CO gr-qc

Sophie Hoyland , Daniela Saadeh , Kazuya Koyama , Harry Desmond This is my paper · ORCID
classification astro-ph.COgr-qc
keywords field-levelinferencemodifiedgravityf(R)galaxybiaslarge-scalestructurecosmicwebCOLAFourierphases
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

Power-spectrum analyses of galaxy clustering cannot cleanly separate the effects of modified gravity from those of galaxy bias, because both can raise or lower clustering amplitude on similar scales. This paper shows that comparing the full three-dimensional galaxy number-count field, voxel by voxel, recovers the missing non-Gaussian and Fourier-phase information and thereby breaks the degeneracy. On controlled mocks with known initial conditions, the field-level Poisson likelihood returns substantially tighter, unbiased constraints on both the Hu–Sawicki parameter |f_R0| and the leading bias parameter β than a power-spectrum analysis of the same data. Under-dense regions (voids and walls) supply most of the distinguishing power. The result is a concrete demonstration that next-generation surveys can test gravity more sharply once the entire map, rather than its two-point summary, is used.

What carries the argument

The full-field Poisson likelihood: each voxel is treated as an independent Poisson draw whose mean is the predicted galaxy count under a given (f_R0, β) model; the global log-likelihood is simply the sum over all voxels, thereby retaining both Fourier amplitudes and phases.

What would settle it

Repeat the identical mock analysis after freely sampling the initial phases (or after replacing the fixed-phase COLA realisations with a full Bayesian reconstruction that marginalises over them) and check whether the |f_R0|–β degeneracy reappears at the power-spectrum level of width.

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Extended reading notes

Core claim

When initial phases are fixed and known, a Bayesian Poisson likelihood evaluated on the three-dimensional galaxy number-count field jointly constrains |f_R0| and the primary bias parameter β more tightly than a Gaussian power-spectrum likelihood and, crucially, breaks the strong degeneracy between the two parameters that is inherent to two-point statistics.

Load-bearing premise

The initial phases of the dark-matter density field are assumed known and fixed; the paper itself notes that marginalising over them on real data is expected to remove the pure-phase information that currently breaks the degeneracy.

Editorial extensions

If this is right

  • Stage-IV surveys can extract substantially tighter joint constraints on gravity and bias by analysing the three-dimensional galaxy field rather than power spectra alone.
  • Cosmic-web classifiers applied to the underlying density field can isolate which environments (especially voids and walls) drive gravity constraints.
  • Phase information alone already prefers the correct |f_R0|; combining it with amplitudes yields the tightest joint posteriors.
  • The same pipeline is modular and can incorporate field-level emulators, more complete bias models, weak lensing, and redshift-space distortions.

Reading between the lines

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

  • Once initial phases must be marginalised, residual field-level gains will come mainly from non-Gaussian amplitude information rather than pure morphology, so hybrid likelihoods that keep higher-order moments may still outperform pure two-point analyses.
  • The finding that n_g = 1 voxels in voids/walls are the most informative suggests that carefully selected void and wall catalogues could serve as cheaper, partially field-level probes even before full map-level inference is routine.
  • Because the degeneracy-breaking is environment-dependent, any residual screening or assembly-bias mismodelling will appear first as spatially coherent residuals in under-dense regions, giving a practical diagnostic for model misspecification.
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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 develops a field-level Bayesian inference pipeline that evaluates a Poisson likelihood directly on the 3D galaxy number-counts field n_g, jointly constraining the Hu–Sawicki |f_R0| and the primary local bias parameter β. Dark-matter fields are generated with MG-extended COLA under fixed initial phases; galaxies are painted with a four-parameter non-linear bias model (only β free, N retuned to keep N_tot fixed). On controlled mocks the full-field analysis yields tighter, less degenerate posteriors than a Gaussian power-spectrum likelihood (Table 1, Fig. 2), isolates the contribution of Fourier phases (§5.4), attributes most of the gain to under-dense voxels via cosmic-web classification (§5.3), and demonstrates robustness to Poisson seeds, initial-condition realisations and number-count thresholding (§6).

Significance. If the controlled demonstration holds, the work supplies a concrete, reproducible illustration that non-Gaussian morphology and phase information can break the classic MG–bias degeneracy that limits two-point analyses. The explicit phase-only versus amplitude-only comparison, the voxel-level likelihood decomposition, and the suite of 100 Poisson + 5 IC robustness tests are genuine strengths that make the result falsifiable and useful for Stage-IV survey forecasts. The transparent scoping to fixed known phases (already flagged by the authors) keeps the claim honest while still charting a path toward BORG-style marginalisation and field-level emulators.

major comments (3)
  1. §5.4 and §7 correctly note that pure-phase information vanishes once initial phases are marginalised, yet the abstract and the final sentence of the conclusions still present the degeneracy-breaking result as a “powerful path forward for au next-generation surveys” without quantifying residual constraining power from non-Gaussian amplitudes alone. A short forecast (or at least a clear statement) of what survives after phase marginalisation is needed for the claim to remain load-bearing outside the idealised setting.
  2. §2.3 and §3.1 fix ρ and ε at the Jasche & Lavaux (2019) values and only vary β (with N retuned). Because the exponential void-suppression term is precisely the piece that couples most strongly to the under-dense voxels identified as the main drivers in §5.3, the reported degeneracy breaking may be optimistic relative to a fully free local (or non-local) bias model. At minimum the authors should show one additional run in which ρ and ε are also free, or justify why the present restriction does not affect the central comparison.
  3. The COLA implementation (§2.2) uses a modest number of time-steps and a linear-field screening approximation. Under-dense regions, which dominate the likelihood ratios in Tables 2–5, are exactly where chameleon screening is weakest and residual force errors are largest. A quantitative comparison of the FML-COLA density field against a full N-body MG run (or a published accuracy benchmark at the same resolution) for the void/wall voxels that drive the constraints would strengthen the claim that the reported |f_R0| posteriors are not resolution artefacts.
minor comments (5)
  1. Fig. 1 (right) correlation matrix and Fig. 3 power-spectrum ratios would benefit from explicit k-bin labels or a second x-axis in h Mpc^{-1} so that the scale dependence of the residual degeneracy is immediately readable.
  2. Eq. (3) and the surrounding text use both n_g and n_g interchangeably; a single consistent notation for the expected galaxy count field would improve readability.
  3. The Percival correction is cited (Percival et al. 2022) but the numerical value of the factor F applied to the 1024-realisation covariance is never stated; a one-line addition in §3.2.1 would aid reproducibility.
  4. Several sentences in the abstract and introduction still contain concatenated words (“Wepresentafield-level ldots”, “Non-linearstructureformation ldots”); these are residual typesetting artefacts that should be cleaned.
  5. Table 1 reports 95 % upper limits for the GR case and 68 % intervals for F6; a uniform confidence level (or an explicit note) would make the comparison cleaner.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: controlled mock comparison of two likelihoods under fixed known phases is self-contained and does not reduce any claim to its inputs by construction.

full rationale

The paper's central demonstration is a side-by-side Bayesian comparison, on the same fixed-seed COLA mocks, of a Gaussian power-spectrum likelihood versus a voxel-wise Poisson field-level likelihood for the joint parameters (β, |f_R0|). Fiducial bias parameters are taken from the external literature (Neyrinck et al. 2014; Jasche & Lavaux 2019 row 11) and held fixed except for the free parameter β; N is retuned solely to keep N_tot constant so that likelihood differences arise only from spatial morphology. No quantity is fitted to a subset of the mock data and then re-labelled a prediction. The phase-only versus amplitude-only tests (Sec. 5.4) and the cosmic-web voxel attribution (Sec. 5.3) are diagnostic analyses of the same likelihood surface, not circular redefinitions. Self-citations (e.g., Hoyland et al. 2025 COLA weak-lensing, Saadeh et al. emulators) appear only in the outlook and are not load-bearing for the reported constraints. The fixed-phase idealisation is explicitly scoped as a limitation (abstract, Sec. 5.4, Sec. 7) rather than hidden. Consequently the derivation chain does not collapse to its inputs by construction, by self-citation, or by renaming.

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

The central claim rests on standard cosmological simulation tools, a literature bias model, and the deliberate idealisation of fixed initial phases. No new physical entities are introduced; free parameters are the usual MG and bias coefficients plus a few fixed nuisance values taken from prior work. The ledger is therefore short and transparent.

free parameters (4)
  • β (primary galaxy bias)
    Varied jointly with |f_R0|; fiducial value 0.77 taken from Jasche & Lavaux (2019) table 2 row 11 and recovered in the inference.
  • |f_R0| (Hu–Sawicki strength)
    Primary MG parameter; sampled on a logarithmic grid from 10^{-8} to 10^{-4} plus GR.
  • N, ρ, ε (remaining bias parameters)
    Fixed to literature values (N=0.19, ρ=1.61, ε=0.09); N is further re-tuned per (β,|f_R0|) pair to keep total galaxy number constant. These choices affect the likelihood surface.
  • Background cosmology (Ω_m, σ_8, _s, _s, h, _s)
    Fixed to Planck 2014 values; not varied.
assumptions (4)
  • domain assumption Galaxy counts in each voxel are independent Poisson draws given the mean predicted by the bias model.
    Used for both full-field and truncated likelihoods (§3.2.2–3.2.3).
  • domain assumption COLA (FML-COLA) with the stated resolution and 2LPT initial conditions is sufficiently accurate for the scales analysed.
    Forward model for all δ_DM fields (§2.2, §3.1).
  • domain assumption The Neyrinck et al. (2014) local-in-density bias model with three parameters fixed is an adequate description of the galaxy–matter relation for this proof-of-concept.
    Eq. 3; authors note non-locality/stochasticity left for future work.
  • ad hoc to paper Initial Gaussian phases are known and identical for all models and the mock data.
    Explicit experimental control that enables the phase-only test and the reported degeneracy breaking; acknowledged as unrealistic for real data (§5.4, §7).

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Cite this review

Pith. "Pith review of Disentangling modified gravity and galaxy bias with field-level inference." pith.science (2026). https://pith.science/paper/UGCNLM57

@misc{pith2026260703514,
  author       = {Pith},
  title        = {Pith review of: Disentangling modified gravity and galaxy bias with field-level inference},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UGCNLM57}},
  note         = {Machine review of arXiv:2607.03514}
}
abstract

We present a field-level inference framework for testing gravity with the large-scale structure that exploits the full information content of the galaxy distribution. Traditional analyses based on the power spectrum discard non-Gaussian and Fourier phase information, resulting in strong degeneracies between modified gravity (MG) and galaxy bias. Our approach overcomes this limitation by performing a Bayesian likelihood analysis directly on the three-dimensional galaxy number counts field, jointly constraining MG and bias parameters using both amplitudes and phases. As an illustrative application, we analyse mock data in the context of the $f(R)$ theory of gravity and a non-linear galaxy bias model. Non-linear structure formation is modelled using the COmoving Lagrangian Acceleration (COLA) method under different gravity strengths, parameterised by $f_{R0}$. The resulting dark matter fields are then mapped to mock galaxy catalogues via a non-linear bias prescription. We demonstrate that, with fixed and known initial phases, including non-Gaussian and phase information yields tighter constraints on both $f_{R0}$ and the primary bias parameter, $\beta$, relative to the power-spectrum-only analyses. Notably, the field-level approach breaks the degeneracies between MG and galaxy bias inherent to two-point statistics. Through a cosmic web classification into voids, walls, filaments and clusters, we find that under-dense regions are the primary drivers in distinguishing gravity models at the field level. Finally, we establish the robustness of our pipeline against variations in initial conditions, Poisson noise, and galaxy field thresholding, providing a powerful path forward for field-level tests of gravity with next-generation surveys.

Figures

Figures reproduced from arXiv: 2607.03514 by the authors.

Figure 1
Figure 1. Left: The galaxy power spectrum, 𝑃g (𝑘), for the GR fiducial model. We show the noiseless theoretical prediction, 𝑃 fid g (𝑘), with 1𝜎 uncertainties estimated from the diagonal of the covariance matrix, C, of 𝑁mock = 1024 independent Poisson-sampled realisations (solid line with error bars). We compare this against the power spectrum measured from the noisy mock data field, 𝑃 obs g (𝑘) (dashed line), and the corresp… view at source ↗
Figure 2
Figure 2. Comparison of constraints on 𝛽 and log10 | 𝑓𝑅0 | obtained with the power spectra of the galaxy number count, 𝑃g (𝑘), and the full-field analysis, 𝑛g. The former uses the Gaussian likelihood in Eq. 8, whereas the latter employs the Poisson likelihood in Eq. 11. Left: GR fiducial mock (true values: log10 | 𝑓𝑅0 | = −∞, 𝛽 = 0.77; prior ranges: 𝛽 ∈ [0.75, 0.80], log10 | 𝑓𝑅0 | ∈ [−8, −4]); Right: F6 fiducial mock (true va… view at source ↗
Figure 3
Figure 3. Ratio of the predicted galaxy power spectra, 𝑃g (𝑘), relative to the fiducial 𝑃 fid g (𝑘), for models indicative of increasing/decreasing galaxy bias (filled/hollow stars, respectively), increasing gravity strength (triangles), and a degeneracy-line model (circles). The specific marker shapes and fills used in this figure exactly match the corresponding models shown in [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Distribution of the fiducial mean galaxy counts, 𝑛 fid g , for given observed integer counts, 𝑛 obs g , in the GR fiducial. The distributions show that voxels with 𝑛 obs g ≥ 1 are predominantly drawn from low-density regions where 𝑛 fid g < 1. This confirms that the Po…
Figure 5
Figure 5. Figure 5: Visualisation of a 2D slice through the simulation volume for GR and F6 fiducial models. Top row: The GR fiducial dataset, showing the DM overdensity, 𝛿 GR DM (left), the cosmic web classification according to 𝛿 GR DM (middle), and the corresponding galaxy number count…
Figure 6
Figure 6. Figure 6: GR fiducial. Slice of the DM density field showing the classification of voxels as voids (left) and walls (right). Lighter regions show the respective cosmic web classification, while darker shaded regions are outside of these structures. Galaxies with 𝑛 obs g = 1 insi…
Figure 7
Figure 7. Figure 7: Constraints on 𝛽 and | 𝑓𝑅0 | obtained by isolating the information content of the Fourier phases for the GR fiducial model (left) and the F6 fiducial model (right). We compare these phase-only constraints (blue) to amplitude-only constraints from the power spectrum usi…
Figure 8
Figure 8. Figure 8: Constraint on 𝛽 and | 𝑓𝑅0 | derived from the full 𝑛 obs g field and cases where a threshold, 𝑇, is applied. Left: GR fiducial, where thresholds on 𝑛 obs g are 𝑇 = 0, 1, 2, 3, 4, 5. Right: F6 fiducial, where thresholds on 𝑛 obs g are 𝑇 = 0, 1, 2, 3, 4. The full-field co…
Figure 9
Figure 9. Figure 9: Constraint on 𝛽 and | 𝑓𝑅0 | from 𝑛g full-field analysis for the F6 fiducial model across 100 Poisson realisations. 6.2 Different Poisson Seeds and DM Initial Conditions We next assess the robustness of our pipeline against stochastic varia￾tions in Poisson noise. For t…

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