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

Very long baseline interferometry (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 classical cosmological test complementary to other distance--redshift methods. Aiming to update and extend previous studies conducted in the 1990s, we analyse a significantly expanded and improved dataset to reassess the angular size--redshift relation and its potential for constraining cosmological model parameters, focusing on the matter density parameter, Ω_ m , in a flat Λ 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. We performed a Markov chain Monte Carlo analysis on real data and on multiple mock catalogues with varying Gaussian noise levels (10%,,20%,, 50%) 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 to explore the statistical significance of the angular size--redshift dependence. We also explored how astrophysical parameters depend on fixed cosmological models with different m values. The randomization test showed that the posterior distributions from randomized data do not overlap with those from real observations, with significant deviations, confirming that the measured angular size--redshift relation is physically meaningful and not a chance alignment. The astrophysical model parameter that describes the redshift dependence of the source angular size exhibits strong sensitivity and degeneracy with Ω_ m . Simulated mock catalogues indicate that the method is able to constrain Ω_ m if the data scatter is below sim20%, but current real data noise levels are too high for reaching competitive cosmological constraints. Scaling estimates suggest that high-quality data of samples of several thousands to ∼ 100,000 sources, a standardization 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 object.