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arxiv: 2606.18437 · v1 · pith:V5AI24E6new · submitted 2026-06-16 · 🌌 astro-ph.CO

Impact of inhomogeneous curvature on growth rate measurements from magnitude fluctuations

Andrew Nguyen , Chris Blake , Hayley J. Macpherson This is my paper

Pith reviewed 2026-06-26 22:55 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords inhomogeneous curvaturegrowth ratemagnitude fluctuationsFLRW metricnumerical relativitypeculiar velocitiescosmological simulationsredshift dependence
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The pith

Inhomogeneous curvature causes only sub-dominant systematic offsets in low-redshift growth rate measurements from magnitude fluctuations.

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

The paper studies how the universe's non-uniform curvature distorts measurements of cosmic structure growth derived from brightness fluctuations of distant objects. It runs full general relativity simulations and compares them directly to standard FLRW models to measure the resulting shifts in the magnitude correlation spectrum at different angles and redshifts. The main result is that below redshift 0.2 these shifts remain smaller than the random errors in today's data sets. This finding justifies continued reliance on homogeneous models for existing peculiar-velocity surveys. Higher-redshift observations will likely need extra terms for lensing and curvature variations.

Core claim

Numerical cosmological simulations generated in full General Relativity show that the systematic offset in growth rate measurements between the full numerical relativity and FLRW treatments is sub-dominant to the statistical error of current datasets at z ≲ 0.2, confirming that FLRW modelling is adequate for current low-redshift peculiar velocity experiments.

What carries the argument

The magnitude correlation spectrum, which encodes angular-scale and redshift-dependent distortions from inhomogeneous curvature and is used to extract the growth-rate systematic offset between GR and FLRW treatments.

If this is right

  • FLRW modelling is adequate for current low-redshift peculiar velocity experiments.
  • Future datasets extending to higher redshift may require theoretical models that additionally incorporate gravitational lensing and inhomogeneous curvature.
  • Distortions in the magnitude correlation spectrum vary with angular scale and redshift.

Where Pith is reading between the lines

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

  • The same conclusion may hold for other low-redshift probes that assume homogeneity.
  • Running the same simulations at higher redshifts would map the redshift where inhomogeneous effects exceed statistical errors.
  • Including curvature inhomogeneity in growth-rate models could refine constraints on dark energy or modified gravity parameters.

Load-bearing premise

The numerical cosmological simulations generated in full General Relativity accurately capture the relevant effects of inhomogeneous spacetime on magnitude fluctuations without significant resolution artifacts or missing physics.

What would settle it

A low-redshift peculiar-velocity survey that yields a growth-rate offset between full-GR and FLRW analyses larger than the reported statistical error would falsify the claim that the systematic offset is sub-dominant.

Figures

Figures reproduced from arXiv: 2606.18437 by Andrew Nguyen, Chris Blake, Hayley J. Macpherson.

Figure 1
Figure 1. Figure 1: Projections of the magnitude fluctuation field δm at redshifts z = 0.1, 0.3, and 0.5 (top to bottom). The left column shows the full NR measurement δmNR, and the right column shows the velocity-only values δmvel calculated using the source and observer velocities. At z = 0.1 the two maps are visually similar, with large-scale features driven dominantly by velocities. At higher redshifts, the amplitude of t… view at source ↗
Figure 2
Figure 2. Figure 2: The angular power spectrum of magnitude fluctuations, Cδm δm ℓ , at a range of redshifts from z = 0.1 to z = 0.6. The green points show the full NR simulation measurement (Cℓ,NR), the purple points show the velocity-only measurements (Cℓ,vel), and the blue and orange curves show the FLRW model prediction due to velocities and lensing, respectively. The errors in the measurements are determined as the stand… view at source ↗
Figure 3
Figure 3. Figure 3: Fisher forecast of the systematic offset ∆f (green) and statistical error σf (purple) in the growth rate, expressed as a percentage of the fiducial value ffid, as a function of redshift for the N = 256 resolution simulation. At z ≤ 0.2 the systematic offset is negligible (< 1%) compared to the statistical error (3–4%). The systematic offset grows rapidly with redshift, reaching ∼8% at z = 0.3, ∼39% at z = … view at source ↗
Figure 4
Figure 4. Figure 4: Angular power spectra of magnitude fluctuations Cδm δm ℓ at redshifts z = 0.1 to z = 0.6 across three simulation resolutions N = {128, 200, 256}. The green points show the NR measurement Cℓ,NR with the lightest green representing the coarsest resolution (N = 128) and the green increasing in darkness as the resolution increases. The purple points show the velocity-only measurement Cℓ,vel with the lightest p… view at source ↗
Figure 5
Figure 5. Figure 5: Convergence test of the systematic offset ∆f (green) and statistical error σf (purple) across three simulation resolutions N = {128, 200, 256}. The systematic offset and the statistical error are converged at N = 256, demonstrating that the measured systematic offset is robust to the simulation resolution. rapidly with redshift, reaching ∼8% at z = 0.3, ∼39% at z = 0.4, and exceeding 100% by z = 0.5, while… view at source ↗
read the original abstract

Our interpretation of current cosmological observations rests on the assumptions of homogeneity and isotropy, leading to uniform background curvature and expansion characterised by the Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime metric. However, the large-scale structure of the Universe is non-uniform in detail, inducing inhomogeneous curvature and scale factor variations. In this paper, we use numerical cosmological simulations generated in full General Relativity to study the impact of inhomogeneous spacetime on the magnitude fluctuations of distant objects, focusing on their use as a probe of the growth rate of cosmic structure. We quantify the distortions in the magnitude correlation spectrum as a function of angular scale and redshift, and use these distortions to infer the systematic offset in the growth rate measurement. We find that at $z \lesssim 0.2$, the systematic offset in growth rate measurements between the full numerical relativity and FLRW treatments is sub-dominant to the statistical error of current datasets, confirming that FLRW modelling is adequate for current low-redshift peculiar velocity experiments. Future datasets extending to higher redshift may require theoretical models that additionally incorporate the contributions of gravitational lensing and inhomogeneous curvature.

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

1 major / 0 minor

Summary. The paper uses numerical cosmological simulations generated in full General Relativity to quantify distortions in the magnitude correlation spectrum induced by inhomogeneous curvature and scale factor variations. These distortions are used to infer the systematic offset in growth rate measurements relative to the standard FLRW prediction. The central claim is that at z ≲ 0.2 the offset is sub-dominant to the statistical error of current datasets, confirming that FLRW modelling is adequate for present low-redshift peculiar velocity experiments, while future higher-redshift data may require models that incorporate gravitational lensing and inhomogeneous curvature.

Significance. If the simulations are shown to be converged and the error analysis complete, the direct numerical comparison between full-GR runs and the FLRW baseline provides a parameter-free test of the robustness of growth-rate inferences from magnitude fluctuations. This strengthens in the adequacy of standard modelling for current low-z datasets and delineates the redshift range where additional physics must be included.

major comments (1)
  1. [Abstract] Abstract: the quantitative conclusion that the systematic offset is sub-dominant to current statistical errors is stated without any information on simulation resolution, convergence tests, error propagation, or the exact definition of the magnitude correlation spectrum. These details are required to verify the central claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their comment highlighting the need for additional context in the abstract to support the central claim. We agree that the abstract would benefit from brief references to key technical aspects and will revise it accordingly while keeping it concise.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the quantitative conclusion that the systematic offset is sub-dominant to current statistical errors is stated without any information on simulation resolution, convergence tests, error propagation, or the exact definition of the magnitude correlation spectrum. These details are required to verify the central claim.

    Authors: We agree that the abstract, being a high-level summary, does not include these specifics. The manuscript body provides the simulation resolution, convergence tests, error propagation details, and the definition of the magnitude correlation spectrum. We will revise the abstract to add a short clause noting the simulation resolution and that convergence has been verified, while directing readers to the main text for the remaining details on error analysis and definitions. This addresses the concern without substantially lengthening the abstract. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper's central claim rests on a direct numerical comparison between full-GR cosmological simulations and standard FLRW modeling of magnitude fluctuations, with the reported offset at z ≲ 0.2 found sub-dominant to statistical errors. This constitutes an independent external benchmark rather than any reduction of the result to a fitted parameter, self-definition, or self-citation chain. No load-bearing steps matching the enumerated circularity patterns are present in the abstract or described methodology; the derivation is self-contained against the simulation outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated beyond the standard assumption of GR and the FLRW background.

pith-pipeline@v0.9.1-grok · 5727 in / 1105 out tokens · 27384 ms · 2026-06-26T22:55:49.366313+00:00 · methodology

discussion (0)

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Reference graph

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