arxiv: 2604.12936 · v1 · submitted 2026-04-14 · 🌌 astro-ph.CO

Recognition: unknown

Revisiting the angular size-redshift cosmological test with milliarcsecond radio structures in active galactic nuclei

Mina Ghodsi Yengejeh , Tatiana A. Koryukova , Leonid I. Gurvits , S\'andor Frey , Alexander B. Pushkarev , Alexander V. Plavin , Kenneth I. Kellermann , Andr\'as Kov\'acs

Authors on Pith no claims yet

Pith reviewed 2026-05-10 14:21 UTC · model grok-4.3

classification 🌌 astro-ph.CO

keywords angular size-redshift relationVLBIactive galactic nucleicosmologymatter densityΛCDMMCMCradio sources

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The pith

VLBI data on compact AGN radio sources shows the angular size-redshift relation is physically real and can constrain Ω_m when scatter is low.

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

This paper re-examines the angular size-redshift test for cosmology using VLBI measurements of milliarcsecond structures in jetted active galactic nuclei, with a dataset an order of magnitude larger than prior studies. The authors apply MCMC fitting to the real data and to mock catalogs, plus a randomization test that shuffles redshifts while keeping other properties fixed. The test reveals that posteriors from real observations do not overlap with those from randomized data, establishing the relation as physically meaningful rather than an artifact of selection. Simulations indicate that the matter density parameter Ω_m in a flat ΛCDM model can be constrained if the scatter stays below about 20 percent, though an astrophysical parameter for source size evolution shows degeneracy with Ω_m.

Core claim

Using an expanded VLBI dataset, the angular size-redshift relation in compact extragalactic radio sources is shown to be physically meaningful because randomized redshift catalogs produce posterior distributions that do not overlap with those from actual observations. Joint MCMC modeling of the relation with an astrophysical parameter describing redshift dependence of source size exhibits degeneracy with Ω_m, but mock catalogs demonstrate that meaningful constraints on Ω_m become possible once observational scatter falls below ∼20 percent. Scaling estimates indicate that samples of several thousand to ∼100,000 sources, together with standardization or refined selection, would be required to

What carries the argument

The angular size-redshift relation for compact radio sources, modeled with a single astrophysical parameter that captures redshift-dependent evolution of intrinsic source size and fitted jointly with Ω_m via MCMC on VLBI angular size measurements.

If this is right

The measured angular size-redshift relation survives a randomization test and therefore reflects real structure rather than chance alignment.
The method yields useful constraints on Ω_m only when the scatter in the angular size measurements remains below approximately 20 percent.
Samples containing several thousand to 100,000 well-measured sources are projected to be necessary before the test can deliver competitive cosmological results.
Standardization calibration of source sizes or stricter selection criteria would be required to reduce the current degeneracy between astrophysical and cosmological parameters.

Where Pith is reading between the lines

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

This radio-based test could be cross-checked against supernova or baryon acoustic oscillation distances to test consistency of the expansion history at high redshift.
Future wide-field VLBI surveys that lower measurement scatter might allow the degeneracy with source evolution to be broken without external calibration.
Once constraints are achieved, the same dataset could be reanalyzed under non-flat or evolving dark-energy models to search for deviations from ΛCDM.

Load-bearing premise

A single adjustable astrophysical parameter can capture the redshift evolution of intrinsic source sizes in a way that remains separable from the geometric effects of cosmology during joint fitting.

What would settle it

If new VLBI data processed with the same MCMC procedure produces Ω_m posteriors that overlap substantially with those from catalogs in which redshifts have been randomly shuffled, the claim that the angular size-redshift relation is physically meaningful would be falsified.

Figures

Figures reproduced from arXiv: 2604.12936 by Alexander B. Pushkarev, Alexander V. Plavin, Andr\'as Kov\'acs, Kenneth I. Kellermann, Leonid I. Gurvits, Mina Ghodsi Yengejeh, S\'andor Frey, Tatiana A. Koryukova.

**Figure 1.** Figure 1: Measured angular sizes (i.e. angular separation between core and jet Gaussian components fitted to the VLBI visibility data) of the AGN at X-band (νobs ≈ [7.6 − 8.7] GHz) in milliarcseconds versus redshift. Each dot represents one source with a median size calculated over all observing epochs together with its error bar, with the filters described in Subsection 2.2 applied. The red points highlight the co… view at source ↗

**Figure 2.** Figure 2: Corner plot showing the marginalized posterior distributions of the model parameters l, β, and n derived from MCMC runs using the Cobaya package for a fixed flat ΛCDM cosmology with H0 = 70 km s−1 Mpc−1 and four values of the matter density parameter: Ωm = 0.2 (red), 0.3 (orange), 0.4 (green), and 0.5 (blue). The contours indicate the 68% and 95% confidence levels. A clear trend is observed across all thre… view at source ↗

**Figure 3.** Figure 3: Corner plot showing the 2D posterior distributions for the parameters l [pc] and n derived from mock catalogues with 10% (olive), 20% (magenta), and 50% (cyan) Gaussian noise. Dashed black lines indicate the fiducial values assumed when generating the mock catalogues. Contours show the degeneracy between l and n, which becomes more elongated with increasing noise, reflecting larger uncertainties along th… view at source ↗

**Figure 4.** Figure 4: Distribution of the best-fit parameters l, β, and n obtained from 100 mock catalogues with randomly shuffled redshifts. The grey histograms represent the null distributions under the assumption of no intrinsic correlation between angular size and redshift. The red vertical lines mark the values of the parameters derived from the real (unshuffled) data: l (9.16 σ), β (8.54 σ), and n (3.51 σ). All three s… view at source ↗

**Figure 5.** Figure 5: The redshift-dependent part of the right-hand side of Equation 8 plotted for different cosmological parameters; DA is measured in Mpc. Top curves for fixed n and varying Ωm = 0.2 (red), 0.3 (orange), 0.4 (green), and 0.5 (blue) with β fixed to the fitted values of [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

read the original abstract

VLBI measurements of the sizes of compact extragalactic radio sources, jetted active galactic nuclei, provide data for probing the angular size--redshift relation, offering a complementary test to other distance--redshift methods. We analyse a significantly expanded dataset to reassess the angular size--redshift relation and its potential for constraining cosmological model parameters, focusing on the matter density parameter $\Omega_{\mathrm{m}}$ in a flat $\Lambda$ Cold Dark Matter Universe. This is the first major update of the compact-source angular size test in the past quarter of a century, using a dataset an order of magnitude larger than in previous studies. MCMC analysis on real data and on multiple mock catalogues to evaluate parameter constraints in the presence of observational scatter. In addition, we conducted a test with 100 randomized catalogues created by shuffling redshifts while preserving other observables. We also explored how astrophysical parameters depend on fixed cosmological models with different $\Omega_{\mathrm{m}}$ values. The randomization test showed that the posterior distributions from randomized data do not overlap with those from real observations, confirming that the measured angular size--redshift relation is physically meaningful. The astrophysical model parameter that describes the redshift dependence of the source angular size exhibits degeneracy with $\Omega_{\mathrm{m}}$. Simulated mock catalogues indicate that the method is able to constrain $\Omega_{\mathrm{m}}$ if the data scatter is below $\sim20\%$. Scaling estimates suggest that high-quality data of samples of several thousands to $\sim 100\,000$ sources, a standardisation calibration approach, and/or refining sample selection criteria are needed to fully exploit the potential of the angular size--redshift test with this type of objects (abridged).

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.

Desk Editor's Note private letter to a colleague

Solid statistical update to the angular-size test with a bigger sample and honest checks, but the degeneracy with the astrophysical parameter keeps cosmological constraints weak for now.

read the letter

The main takeaway is that this is a careful modern re-run of the classic angular size-redshift test using VLBI compact sources. They have an order-of-magnitude larger dataset than the last serious attempts twenty-five years ago, and they add randomization tests plus mock catalogues to validate the signal. The randomization (shuffling redshifts) produces posteriors that do not overlap with the real data, which shows the measured relation is not noise or selection artifact. That part is done cleanly and is worth noting.

Referee Report

2 major / 2 minor

Summary. The manuscript analyzes an expanded VLBI dataset of milliarcsecond-scale radio structures in jetted AGN to revisit the angular size-redshift relation as a cosmological test for Ω_m in flat ΛCDM. MCMC is used to jointly fit Ω_m and an astrophysical parameter governing redshift evolution of intrinsic source size; validation employs mock catalogs (to assess scatter thresholds) and 100 randomized catalogs (redshifts shuffled while preserving other observables). The randomization test shows non-overlapping posteriors relative to real data, and mocks indicate Ω_m constraints are feasible for scatter ≲20%. Degeneracy between the astrophysical parameter and Ω_m is noted, with the conclusion that samples of thousands to ~100,000 sources plus standardization or refined selection are required.

Significance. The update with an order-of-magnitude larger sample and modern statistical validation (MCMC, mocks, randomization) strengthens the case that a physical angular size-redshift signal exists in compact radio sources. If the degeneracy can be controlled and selection systematics quantified, the method offers a potential independent distance probe; the explicit demonstration that low scatter enables Ω_m recovery is a concrete, falsifiable result.

major comments (2)

[Randomization test and MCMC fitting procedure] The randomization test (shuffling redshifts while keeping other observables) demonstrates that the observed θ(z) trend is not an artifact of the redshift distribution alone. However, because both the astrophysical evolution parameter and Ω_m enter the predicted angular size through the same angular-diameter distance, this test does not establish that the two parameters are separable; the non-overlap of posteriors only confirms a redshift-dependent signal exists, not that marginal constraints on Ω_m are data-driven rather than prior-driven.
[Mock catalogue analysis] Mock-catalogue results indicate that Ω_m can be recovered when scatter is below ~20%. Because the mocks are constructed with the identical functional form for size evolution and the same scatter model assumed in the real-data fit, they cannot diagnose bias or loss of constraining power due to model misspecification, unmodeled selection effects in the VLBI sample, or deviations from the assumed linear (or power-law) redshift dependence.

minor comments (2)

[Abstract] The abstract states that 'scaling estimates suggest' larger samples are needed; a short quantitative scaling relation or table showing how constraint width scales with sample size and scatter would make this claim more concrete and easier to evaluate.
[Methods and results] Notation for the astrophysical evolution parameter (e.g., whether it is a power-law index n in (1+z)^n or a linear coefficient) should be defined explicitly at first use and used consistently in equations and figures.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the scope and limitations of our analysis. We respond point-by-point below and have revised the manuscript to address the concerns raised.

read point-by-point responses

Referee: The randomization test (shuffling redshifts while keeping other observables) demonstrates that the observed θ(z) trend is not an artifact of the redshift distribution alone. However, because both the astrophysical evolution parameter and Ω_m enter the predicted angular size through the same angular-diameter distance, this test does not establish that the two parameters are separable; the non-overlap of posteriors only confirms a redshift-dependent signal exists, not that marginal constraints on Ω_m are data-driven rather than prior-driven.

Authors: We appreciate the referee highlighting this important nuance. The randomization test was designed to demonstrate that the angular size-redshift trend is not an artifact of the redshift distribution in the sample. We agree that, given the shared dependence on angular-diameter distance, the test does not fully establish separability of the astrophysical and cosmological parameters, nor does it prove that marginal Ω_m constraints are entirely data-driven. In the revised manuscript we will expand the relevant discussion to explicitly note this limitation, emphasize the acknowledged degeneracy, and present the joint posterior more clearly so readers can assess the role of priors. revision: partial
Referee: Mock-catalogue results indicate that Ω_m can be recovered when scatter is below ~20%. Because the mocks are constructed with the identical functional form for size evolution and the same scatter model assumed in the real-data fit, they cannot diagnose bias or loss of constraining power due to model misspecification, unmodeled selection effects in the VLBI sample, or deviations from the assumed linear (or power-law) redshift dependence.

Authors: We agree that the mock catalogues, by construction, assume the same functional form and scatter model used in the fits and therefore assess statistical power under the adopted model rather than testing for biases from misspecification or unmodeled VLBI selection effects. In the revised manuscript we will add an explicit caveat in the discussion section stating that the reported scatter threshold and required sample sizes are conditional on the validity of the assumed size-evolution model, and we will note that future work should explore alternative parametrizations and quantify selection systematics. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation or validation chain

full rationale

The paper performs standard MCMC joint fitting of the cosmological parameter Ω_m together with an astrophysical evolution parameter on observed angular-size and redshift data from VLBI sources. It validates the presence of a physical signal via a redshift-shuffling randomization test and assesses recoverability via mock catalogues generated under controlled scatter. No equation or procedure reduces the reported constraints to a self-definition, a fitted quantity renamed as an independent prediction, or a load-bearing self-citation. The acknowledged degeneracy between the astrophysical and cosmological parameters is treated as a statistical feature of the joint fit rather than hidden by construction; the randomization and mock tests remain independent of that degeneracy. The overall chain therefore rests on external data and conventional Bayesian inference without internal circular reduction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on modeling the angular size as a function of redshift with an astrophysical evolution parameter that is fitted jointly with cosmology; this parameter is the primary free parameter and source of degeneracy. The assumption that source sizes follow a predictable redshift dependence independent of cosmology is a domain-level premise.

free parameters (1)

astrophysical redshift dependence parameter
Parameter in the model for how source angular size evolves with redshift; fitted from data and degenerate with Ω_m.

axioms (1)

domain assumption Compact extragalactic radio sources have a redshift-dependent angular size evolution that can be parameterized separately from cosmological geometry
Invoked to enable the angular size-redshift test; stated implicitly in the use of the relation to constrain Ω_m.

pith-pipeline@v0.9.0 · 5662 in / 1472 out tokens · 92232 ms · 2026-05-10T14:21:52.908708+00:00 · methodology

discussion (0)

Reference graph

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2017