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

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).