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

Technical Summary: Forward-modelling the Tolman and distance-duality tests with IllustrisTNG

Problem Statement
Recent observational results have presented signals that appear to challenge the standard $\Lambda$CDM cosmological model and the Etherington distance-duality relation ($D_L = (1+z)^2 D_A$). Specifically, JWST/ASTRODEEP measurements of surface brightness (SB) suggest a redshift scaling much flatter than the expected $(1+z)^{-4}$ (bolometric) or $(1+z)^{-(3+\alpha_{SED})}$ (specific flux) for non-evolving sources. Similarly, analyses of ultracompact radio sources suggest a distance-duality ratio ($D_L/D_A$) scaling closer to $(1+z)$ rather than $(1+z)^2$. While these findings have been interpreted by some as evidence for non-expanding cosmologies (e.g., tired-light models), they are also sensitive to astrophysical source evolution and instrumental systematics. The core problem addressed is whether these "anomalies" can be explained by intrinsic luminosity and size evolution within standard Friedmann–Robertson–Walker (FRW) cosmology, or if they necessitate a breakdown of metric gravity.

Methodology
The authors employ a forward-modelling approach using the IllustrisTNG-100 cosmological hydrodynamical simulation to test the hypothesis that source evolution, rather than non-standard cosmology, drives the observed signals.

1. Data Sources:

   • Observational: The ASTRODEEP-JWST catalogue (Merlin et al. 2024) for the Tolman test and the Li (2023) compilation of ultracompact radio sources (JJ2.29 and GKF5.0) for the distance-duality test (DDR).
   • Simulation: The IllustrisTNG-100-1 run, utilizing mock HST/JWST imaging from the MAST archive.

2. Mock Spectroscopic Selection:
   Since the TNG simulation lacks real spectra, the authors trained a binary logistic-regression classifier on the ASTRODEEP catalogue to predict the probability ($p_{spec}$) that a galaxy would receive a confirmed spectroscopic redshift based on its photometric properties (magnitudes, colors, surface brightness, aperture area, and redshift proxy). This classifier was applied to TNG mock galaxies to create a "mock-spectroscopic" sample that mimics the selection biases of the real observational data.

3. Forward Modelling of Evolution:
   The study defines two distinct evolution exponents:

   • $\gamma_\Sigma$: The exponent for projected luminosity density ($\Sigma_L \propto (1+z)^{\gamma_\Sigma}$), which governs the Tolman SB test.
   • $\gamma_\rho$: The exponent for volumetric luminosity density ($\rho_L \propto (1+z)^{\gamma_\rho}$), which governs the DDR test under the Li (2023) compact-source assumption.

   The authors calculate these exponents in the TNG simulation using four different aperture conventions (catalogue flux, fixed circular image aperture, Voronoi-deblended image aperture, and adaptive aperture) to quantify systematic uncertainties. They then map the simulated exponents to the observable scaling parameters ($\alpha_{Tol}$ and $\alpha_{DDR}$) to compare directly with observational data.

4. Systematic Checks:
   The analysis includes rigorous checks on redshift distribution matching, aperture definitions, deblending algorithms (Voronoi vs. Gaussian), PSF convolution, sky noise, and cosmic variance.

Key Results

• Unification of Evolution Terms: In the TNG simulation, the projected luminosity density exponent ($\gamma_\Sigma$) and the volumetric luminosity density exponent ($\gamma_\rho$) are found to be effectively identical for the matched bright-galaxy sample ($\gamma_\Sigma \approx \gamma_\rho$). This allows the two distinct tests to be unified under a single effective evolution exponent, $\gamma$.
• Simulated Evolution Value: Across realistic aperture conventions, the TNG simulation yields an effective luminosity-density evolution exponent of $\gamma = 2.23 \pm 0.20$.
• Reproduction of Observational Signals:
  • Tolman Test: The TNG forward model produces a Tolman slope ($\alpha_{Tol}$) of $-0.88 \pm 0.03$ (Voronoi-deblended), which is significantly flatter than the no-evolution FRW prediction of $-3.3$ (for $\alpha_{SED}=0.3$) and closely matches the observed ASTRODEEP slope of $-1.28 \pm 0.05$.
  • Distance-Duality Test: The TNG-derived $\gamma$ predicts a DDR slope of $\alpha_{DDR} \approx 1.26$, which is in good agreement with the radio-source data value of $\alpha_{DDR} = 1.17 \pm 0.09$ (corresponding to $\gamma = 2.50 \pm 0.26$).
• Discrepancy Analysis: A small residual discrepancy exists between the TNG bright-galaxy $\gamma$ and the radio-source $\gamma$ ($\Delta\gamma \approx 0.27 \pm 0.33$). The authors interpret this as a potential indication that compact radio AGN evolve slightly more strongly in luminosity density than the bright galaxies modeled in TNG, rather than a failure of the cosmological model.
• Normalization Clarification: The paper demonstrates that the apparent alignment of radio data with the "non-expanding" line ($D_L = (1+z)D_A$) in previous studies is an artifact of the arbitrary normalisation convention used for the rest-frame size scale ($d_0$). When viewed in terms of the slope alone, the data lie between the no-evolution FRW prediction and the non-expanding limit, not strictly on the latter.

Significance and Claims
The paper claims that the "anomalies" reported in recent Tolman and distance-duality tests do not require modifications to standard cosmology or the introduction of non-expanding models. Instead, the results are fully consistent with standard $\Lambda$CDM galaxy formation physics, where intrinsic source evolution (specifically the increase in luminosity density with redshift) naturally produces the observed shallow scaling slopes.

The authors conclude that:

1. The Tolman and DDR results are not independent anomalies requiring a coordinated cosmological explanation but are two measurements of the same underlying source evolution.
2. The magnitude of this evolution is correctly predicted by the IllustrisTNG simulation.
3. The data do not unambiguously support a non-expanding universe; rather, they lie in a regime intermediate between no-evolution FRW and non-expanding models.
4. Future cosmological inferences from these tests require precise calibration of source evolution and photometric systematics (particularly aperture definitions and deblending) rather than a revision of the metric theory of gravity.

The work reframes these tests as probes of high-redshift galaxy evolution and the systematics inherent in measuring them, offering a path to constrain galaxy formation models without invoking new physics.