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arxiv: 2606.01529 · v2 · pith:YX6SA7KFnew · submitted 2026-06-01 · 🌌 astro-ph.CO

Optimal Transport Reconstruction of Biased Tracers in Primordial Non-Gaussian Fields

Farnik Nikakhtar , Ravi K. Sheth , Nikhil Padmanabhan , Bruno L\'evy , Roya Mohayaee This is my paper

Pith reviewed 2026-06-28 13:35 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords optimal transportprimordial non-Gaussianitybiased tracersreconstruction methodslarge-scale structureinitial conditionsdust modeling
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The pith

Optimal transport reconstruction of initial conditions from biased tracers in local primordial non-Gaussian fields improves when the unseen mass is modeled with its own scale-dependent bias.

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

The paper establishes that optimal transport can map biased tracers back to their initial positions even when the primordial density field carries local non-Gaussianity. It does so by noting that the scale-dependent clustering signature induced by the product of f_NL and tracer bias appears only in the measured subset and is absent from the complete matter distribution. The unseen mass, treated as dust, therefore carries a compensating scale dependence of different amplitude. When this dust is assigned a more realistic clustering model, the accuracy of the reconstructed initial displacement field increases. A reader would care because the approach offers a way to recover early-universe information from incomplete large-scale structure catalogs without assuming Gaussian initial conditions.

Core claim

For local primordial non-Gaussianity, the large-scale clustering of biased tracers carries a scale-dependent signature proportional to f_NL times b_phi that is absent from the full matter field. Optimal transport reconstruction exploits this difference by assigning the unseen mass a dust component with its own characteristic scale dependence; the quality of the recovered initial positions improves as the model for this dust is made more realistic.

What carries the argument

The optimal transport map from observed positions of biased tracers to initial positions, extended by treating the unseen mass as dust whose scale-dependent bias compensates for the signature present only in the tracers.

If this is right

  • The method recovers initial conditions without requiring the displacement field itself to be Gaussian.
  • Reconstruction error decreases once the dust component is assigned a scale-dependent bias whose amplitude differs from that of the tracers.
  • The approach isolates the product f_NL times b_phi through the difference between tracer and full-field clustering.
  • The reconstruction remains valid for the class of local primordial non-Gaussian models currently of interest in cosmology.

Where Pith is reading between the lines

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

  • Surveys that measure both galaxies and the total mass (via weak lensing or intensity mapping) could supply an empirical dust model that further tightens the reconstruction.
  • The same logic may apply to other forms of primordial non-Gaussianity whose bias signatures are also absent from the full field.
  • If the dust model can be calibrated on small scales where non-Gaussian effects are weaker, the method could be applied to progressively larger survey volumes.

Load-bearing premise

The scale-dependent clustering signature induced by local non-Gaussianity is present in biased tracers but absent from the complete matter field.

What would settle it

A set of N-body simulations with known local non-Gaussian initial conditions in which the reconstruction error on the initial displacement field fails to decrease when the dust model is switched from a constant bias to a scale-dependent bias matching the full field.

Figures

Figures reproduced from arXiv: 2606.01529 by Bruno L\'evy, Farnik Nikakhtar, Nikhil Padmanabhan, Ravi K. Sheth, Roya Mohayaee.

Figure 2
Figure 2. Figure 2: FIG. 2. At small [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Scale dependent bias of the pre- (upper solid curves) [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Bias of the full matter field pre- (dotted curves) and [PITH_FULL_IMAGE:figures/full_fig_p003_5.png] view at source ↗
read the original abstract

Optimal transport provides an efficient method to infer the displacement of objects by mapping their initial positions to their present-day locations over cosmic time; equivalently, it enables the reconstruction of initial positions from measurements taken at later times. The method has been shown to be accurate even if positions for only a biased subset of the particles are measured, provided that the initial displacement field was Gaussian. The method does not rely on the assumption of a Gaussian displacement field, and thus may be extended to the reconstruction of non-Gaussian initial conditions. Here, we demonstrate how this is achieved for a class of "local" primordial non-Gaussian fields of current interest in cosmology. For these models, there is a distinctive signature in the large scale clustering of biased tracers which depends on the product of the primordial amplitude $f_{\rm NL}$ and the nature of the tracers $b_\phi$. Our method exploits the fact that this signature is not present in the full field; it is only present in biased fields. Therefore, the mass that is not in the biased subset, what we call the "dust", also has a characteristic scale-dependence, albeit of a different amplitude. We show that the quality of the optimal transport reconstruction improves as the model for this dust becomes more realistic.

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

0 major / 2 minor

Summary. The manuscript extends optimal transport reconstruction of initial conditions to local primordial non-Gaussianity (PNG) models. It exploits the absence of the f_NL b_phi scale-dependent bias signature in the full matter field (present only in biased tracers) to assign a compensating scale dependence to the unobserved 'dust' mass, and claims that reconstruction quality improves as the dust model becomes more realistic.

Significance. If the central result holds, the work provides a mass-conserving, non-Gaussian-displacement extension of OT methods that could improve initial-condition reconstruction for f_NL constraints from biased tracers in large-scale structure surveys. The approach is internally consistent with standard local PNG perturbation theory and does not introduce free parameters or circular definitions.

minor comments (2)
  1. [Abstract] Abstract: the claim that reconstruction quality 'improves as the model for this dust becomes more realistic' would be strengthened by a quantitative metric (e.g., displacement error or power-spectrum recovery) even in the abstract or a summary table.
  2. The manuscript should explicitly state the specific local PNG template (e.g., the form of the potential or the bispectrum shape) used in the demonstration to allow direct comparison with existing f_NL forecasts.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our work and for recommending minor revision. No specific major comments were raised in the report, so we have no point-by-point responses to provide. We will address any minor issues identified during the revision process.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The derivation chain is self-contained and does not reduce any central claim to a fitted parameter, self-definition, or load-bearing self-citation. The method exploits the established distinction from local PNG perturbation theory that the f_NL b_phi scale-dependent bias appears only in biased tracers and is absent from the unbiased matter field at linear order; this is an external input, not derived within the paper. Optimal transport reconstruction is then applied to the complementary dust component with a compensating scale dependence, with no equations shown to be tautological by construction or renamed known results. The abstract and description present an extension that relies on mass conservation and field properties rather than internal fitting loops.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 1 invented entities

Based solely on the abstract, the central claim rests on the existence of a compensating scale-dependent signature in the unobserved dust and on the assumption that modeling it improves reconstruction; no free parameters or invented entities beyond the dust concept are quantified.

invented entities (1)
  • dust no independent evidence
    purpose: the mass not in the biased subset that carries a compensating scale-dependent clustering signature
    Introduced to explain why the biased-tracer signature is absent from the full field; independent evidence not provided in abstract.

pith-pipeline@v0.9.1-grok · 5775 in / 1169 out tokens · 29993 ms · 2026-06-28T13:35:44.639571+00:00 · methodology

discussion (0)

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Reference graph

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