The use of ultra-compact radio sources for the angular size-redshift cosmological test

Using a sample of radio sources observed with Very Long Baseline Interferometry (VLBI) and the standard cosmological model, it is shown that the cores of radio sources observed with ground-based VLBI with resolutions of the order of several milliarcseconds (which serve as ultra-compact radio sources) cannot be used as "standard rulers" in the angular size-redshift cosmological test. This is a consequence of the insufficient resolution of ground-based VLBI arrays and the flux-limited nature of the radio samples used. In this case, the luminosity-linear size correlation detected in many studies of VLBI source samples has an instrumental origin, in contrast to the analogous correlation for radio galaxies and quasars on angular scales of several arcseconds.