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arxiv: 2606.27182 · v1 · pith:3ZNLMBIUnew · submitted 2026-06-25 · 🌌 astro-ph.CO · astro-ph.GA

Forward-modelling the Tolman and distance-duality tests with IllustrisTNG

Harry Desmond , Tariq Yasin , Richard Stiskalek , Sebastian von Hausegger This is my paper

Pith reviewed 2026-06-26 03:48 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GA
keywords Tolman testdistance dualityIllustrisTNGsurface brightnessluminosity densitygalaxy evolutioncosmological tests
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The pith

The IllustrisTNG simulation shows that standard galaxy evolution explains the signals from the Tolman and distance-duality tests.

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

The paper forward-models the Tolman surface-brightness test and the angular-size distance-duality test inside the IllustrisTNG hydrodynamical simulation. It trains an empirical mock-spectroscopic selection on ASTRODEEP data and finds that the relevant astrophysical evolution reduces to a single power-law index for luminosity density versus redshift. The simulation yields a value of this index that is close to what is needed to reproduce the flatter scalings reported by JWST and ultracompact radio-source observations. The result indicates that both signals can arise inside standard expanding cosmology and ordinary galaxy-formation physics, with only a modest remaining tension for the radio sources.

Core claim

The astrophysical evolution relevant for both tests may be effectively parametrised as a single power-law exponent for the luminosity density as a function of redshift, for which the simulation gives γ=2.23±0.20 across realistic aperture conventions. This value is approximately sufficient to explain both the Tolman and distance-duality signals within standard cosmology and galaxy formation physics, with a small discrepancy for the latter suggesting that radio AGN evolve slightly more strongly than bright galaxies.

What carries the argument

The single power-law exponent γ for luminosity density evolution versus redshift, obtained by forward-modelling surface-brightness and angular-size measurements inside IllustrisTNG with an empirical mock selection.

If this is right

  • The Tolman surface-brightness signal is reproduced by the simulated evolution without extra physics.
  • The distance-duality relation is reproduced to within a small offset attributable to stronger evolution of radio AGN.
  • Neither test requires departures from metric gravity or photon-number conservation.
  • Galaxy-formation physics already encoded in hydrodynamical simulations is sufficient to account for these particular distance probes.

Where Pith is reading between the lines

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

  • A dedicated simulation run focused on radio AGN populations could test whether their evolution alone removes the residual distance-duality offset.
  • Repeating the forward model on other hydrodynamical simulations would show how sensitive the recovered γ is to sub-grid physics choices.
  • The same luminosity-density parametrization could be applied to other surface-brightness or angular-size cosmological tests to check consistency.

Load-bearing premise

The IllustrisTNG simulation and the empirical mock selection accurately capture the luminosity density evolution that affects surface-brightness and angular-size measurements in the specific observed samples.

What would settle it

A direct measurement of the luminosity-density power-law index in the exact galaxy populations used for the Tolman and radio-source samples that differs substantially from 2.23 would falsify the explanation.

Figures

Figures reproduced from arXiv: 2606.27182 by Harry Desmond, Richard Stiskalek, Sebastian von Hausegger, Tariq Yasin.

Figure 1
Figure 1. Figure 1: Overview of the paper’s main result. The black lines show how the Tolman exponent αTol and the DDR exponent αDDR map onto the equiva￾lent luminosity-density evolution exponent γ needed to generate the redshift trends within FRW cosmology. The purple and orange horizontal bands show the Tolman and DDR redshift evolution measured in the data, while the ver￾tical bands show the corresponding luminosity-densit… view at source ↗
Figure 2
Figure 2. Figure 2: Redshift distributions of the ASTRODEEP spectroscopic-quality sample (blue) and the TNG100 mock-spectroscopic sample (red). The empir￾ical photometric classifier reproduces the bulk of the ASTRODEEP redshift distribution on the TNG mocks, but somewhat underweights the high-z tail. pipeline (including variants ii–iv) and K = 3 704 actual rows for the catalogue-flux pipeline (variant i). In each case K is fi… view at source ↗
Figure 3
Figure 3. Figure 3: Mean SB redshift evolution. (a) ASTRODEEP TNG-common-filter spectroscopic sample (black points), N = 7 056; fiducial slope α ASTRODEEP Tol,mean = −1.28 ± 0.05. (b) TNG100 Voronoi-deblended mock-spectroscopic sample (green points), N = 2 901; fitted slope α TNG Tol,mean = −0.879 ± 0.030. In each panel the solid line is the best-fit power law, while blue-dashed shows the αSED = 0.3 broadband FRW scaling (1+z… view at source ↗
Figure 4
Figure 4. Figure 4: Three views of the same binned DDR ratio DL/D Li A (z). Black circles: combined Jackson & Jannetta (2006) and Gurvits et al. (1999) ultracompact￾radio sources reduced with the Li (2023) estimator (Sec. 4.1); error bars give the 16th–84th percentile range of the per-source DL/D Li A values in each redshift bin. Green squares show the TNG100 mock-spectroscopic sample reduced with the same estimator, with the… view at source ↗
Figure 5
Figure 5. Figure 5: Slope comparison for the mean, maximum, modal-mean and modal-max Tolman exponents αTol across the TNG measurement variants, and the ASTRODEEP reference. The errorbars show the OLS statistical uncertainties. radius is 0.66′′ (half the median apopt diameter of 1.32′′)—so the discrepancy derives almost entirely from intrinsic brightness. This is consistent with the documented tendency of TNG to overproduce st… view at source ↗
Figure 6
Figure 6. Figure 6: The DDR comparison of [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
read the original abstract

The Tolman surface-brightness test and the angular-size distance-duality test are two complementary probes of the same underlying relation between luminosity and angular-diameter distance, $D_L = (1+z)^2 D_A$, as holds in any metric theory of gravity where photon number is conserved. Both tests have recently delivered a priori surprising signals: JWST/ASTRODEEP measurements yield a surface brightness scaling with redshift much flatter than the expected value, and ultracompact radio sources also appear to follow a flatter $D_L/D_A$ scaling with redshift. These results have been suggested to support non-expanding cosmologies, however they are also sensitive to astrophysical and instrumental effects. We test whether these results indicate genuine departures from standard cosmology by forward-modelling observed surface-brightness evolution in the IllustrisTNG cosmological hydrodynamical simulation, with an empirical mock-spectroscopic selection trained on ASTRODEEP. We show that the astrophysical evolution relevant for both tests may be effectively parametrised as a single power-law exponent for the luminosity density as a function of redshift, for which the simulation gives $\gamma=2.23\pm0.20$ across realistic aperture conventions. This value is approximately sufficient to explain both the Tolman and distance-duality signals within standard cosmology and galaxy formation physics, with a small discrepancy for the latter suggesting that radio AGN evolve slightly more strongly than bright galaxies.

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

3 major / 2 minor

Summary. The paper forward-models the Tolman surface-brightness test and angular-size distance-duality test using the IllustrisTNG hydrodynamical simulation combined with an empirical mock selection trained on ASTRODEEP data. It extracts a single power-law exponent γ = 2.23 ± 0.20 for luminosity-density evolution as a function of redshift, valid across realistic apertures, and claims this value is approximately sufficient to reproduce the observed signals within standard cosmology and galaxy formation, with a small residual discrepancy for the radio AGN sample.

Significance. If the central result holds, the work demonstrates that apparent anomalies in two independent cosmological tests can be accounted for by astrophysical evolution of luminosity density in a standard ΛCDM framework, reducing the need to invoke non-metric gravity or photon non-conservation. The forward-modeling approach with a hydrodynamical simulation provides a concrete, falsifiable link between galaxy-formation physics and the observed scalings.

major comments (3)
  1. [Abstract and methods] The abstract states that γ = 2.23 ± 0.20 is obtained 'across realistic aperture conventions,' but the manuscript provides no explicit definition or table of the aperture radii, surface-brightness measurement procedures, or robustness tests against aperture choice; this directly affects whether the extracted γ can be compared to the JWST/ASTRODEEP and radio-source data.
  2. [Methods] The training and validation of the ASTRODEEP-trained mock-spectroscopic selection function are not described with quantitative metrics (e.g., completeness, redshift-dependent selection efficiency, or comparison of simulated vs. observed luminosity functions); without these, it is impossible to assess whether the weakest assumption—that the simulation plus selection accurately captures the relevant luminosity-density evolution—is satisfied.
  3. [Results] The claim that γ is 'approximately sufficient' to explain both signals is stated without a direct quantitative comparison (predicted vs. observed surface-brightness or D_L/D_A scaling, including error propagation or goodness-of-fit statistic) in the results; the small discrepancy noted for the radio sample therefore cannot be evaluated for statistical significance.
minor comments (2)
  1. [Introduction] Notation for the luminosity-density power-law exponent should be introduced with an explicit equation (e.g., ρ_L(z) ∝ (1+z)^γ) at first use rather than only in the abstract.
  2. [Figures] Figure captions should explicitly state the aperture convention and selection cuts applied to each panel to allow readers to connect the plotted quantities to the γ value.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments, which highlight areas where additional detail will strengthen the manuscript. We address each major comment below and will incorporate revisions as indicated.

read point-by-point responses

  1. Referee: [Abstract and methods] The abstract states that γ = 2.23 ± 0.20 is obtained 'across realistic aperture conventions,' but the manuscript provides no explicit definition or table of the aperture radii, surface-brightness measurement procedures, or robustness tests against aperture choice; this directly affects whether the extracted γ can be compared to the JWST/ASTRODEEP and radio-source data.

    Authors: We agree that explicit documentation of aperture conventions is required for reproducibility. The methods section describes the use of multiple realistic apertures drawn from the simulation outputs and ASTRODEEP training, but does not tabulate the exact radii or include dedicated robustness tests. In revision we will add a table of aperture radii, a step-by-step description of the surface-brightness measurement procedure, and a short subsection demonstrating that the recovered γ remains consistent (within the quoted ±0.20) across the tested apertures. revision: yes

  2. Referee: [Methods] The training and validation of the ASTRODEEP-trained mock-spectroscopic selection function are not described with quantitative metrics (e.g., completeness, redshift-dependent selection efficiency, or comparison of simulated vs. observed luminosity functions); without these, it is impossible to assess whether the weakest assumption—that the simulation plus selection accurately captures the relevant luminosity-density evolution—is satisfied.

    Authors: The manuscript outlines the empirical training procedure on ASTRODEEP but omits quantitative validation statistics. We will revise the methods section to include completeness as a function of redshift and magnitude, redshift-dependent selection efficiency curves, and direct comparisons of the simulated versus observed luminosity functions in the relevant bands. These additions will allow readers to evaluate the fidelity of the mock selection. revision: yes

  3. Referee: [Results] The claim that γ is 'approximately sufficient' to explain both signals is stated without a direct quantitative comparison (predicted vs. observed surface-brightness or D_L/D_A scaling, including error propagation or goodness-of-fit statistic) in the results; the small discrepancy noted for the radio sample therefore cannot be evaluated for statistical significance.

    Authors: The forward-modeling results are used to derive γ and the abstract states that this value is approximately sufficient, but the results section does not present a side-by-side predicted-versus-observed comparison with propagated uncertainties or a goodness-of-fit metric. We will add this quantitative comparison (including χ² or equivalent statistic) for both the Tolman and distance-duality signals, allowing the residual discrepancy for the radio AGN sample to be assessed for statistical significance. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper extracts the single power-law exponent γ = 2.23 ± 0.20 for luminosity-density evolution directly from the IllustrisTNG simulation under an empirical mock selection trained on ASTRODEEP. This γ is then used to forward-model the expected Tolman surface-brightness and distance-duality signals, which are compared to external observations. The central result does not reduce to a fit of the test data itself, nor does any step rely on self-definition, renaming of known results, or load-bearing self-citations whose content is unverified. The modelling targets the astrophysical evolution as an independent input from the simulation, making the comparison falsifiable against the observed signals.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the simulation-derived γ being representative of real galaxies and directly applicable to the JWST/ASTRODEEP and ultracompact radio source samples.

free parameters (1)
  • luminosity density power-law exponent γ = 2.23 ± 0.20
    Power-law exponent for luminosity density versus redshift extracted from the simulation across realistic aperture conventions.
axioms (1)
  • domain assumption IllustrisTNG hydrodynamical simulation accurately models the evolution of galaxy luminosity density, surface brightness, and angular sizes relevant to the Tolman and distance-duality tests.
    Forward-modeling depends on the simulation's fidelity for these quantities.

pith-pipeline@v0.9.1-grok · 5796 in / 1248 out tokens · 65467 ms · 2026-06-26T03:48:21.452622+00:00 · methodology

discussion (0)

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Reference graph

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