Very Long Baseline Interferometry (VLBI) allows us to study a core of AGN with a sub-parsec resolution. We analyze the dependencies "apparent angular size -redshift" and "apparent motion -redshift" which contain an imprint of the source's properties and cosmology. We present data on the "angular size -redshift" relation obtained with VLBI at 5 GHz on a sample of 300 AGN distributed over the widest available range of redshifts 0.016 < ζ < 4.5. The sample exceeds those used in similar studies earlier by Kellermann (1993, 79 sources) and Wilkinson et al. (1997, 160 sources). Unlike extended source, the angular size-redshift for compact radio sources appears consistent with the predictions of standard FViedmann world models with q 0 ~ 0.5 without taking into account evolutionary effects or selection effects due to a "linear size -luminosity" or "linear sizespectral index" dependences. We discuss different approaches allowing us to disentangle intrinsic evolutionary properties of sources and parameters of the cosmological model. Recent estimates of parameters of the cosmological model are given. We also discuss a perspective of conclusive cosmological tests using the VLBI technique. LIG acknowledges support from the EU under contract CHGECT 920011 and a travel grant from the Leids Kerkhoven Boscha Fond.

The quest for binary and dual supermassive black holes (SMBHs) at the dawn of the multi-messenger era is compelling. Detecting dual active galactic nuclei (AGN)-active SMBHs at projected separations larger than several parsecs-and binary AGN-probing the scale where SMBHs are bound in a Keplerian binary-is an observational challenge. The study of AGN pairs (either dual or binary) also represents an overarching theoretical problem in cosmology and astrophysics. The AGN triggering calls for detailed knowledge of the hydrodynamical conditions of gas in the imminent surroundings of the SMBHs and, at the same time, their duality calls for detailed knowledge on how galaxies assemble through major and minor mergers and grow fed by matter along the filaments of the cosmic web. This review describes the techniques used across the electromagnetic spectrum to detect dual and binary AGN candidates and proposes new avenues for their search. The current observational status is compared with the state-of-the-art numerical simulations and models for formation of dual and binary AGN. Binary SMBHs are among the loudest sources of gravitational waves (GWs) in the Universe. The search for a background of GWs at nHz frequencies from inspiralling SMBHs at low redshifts, and the direct detection of signals from their coalescence by the Laser Interferometer Space Antenna in the next decade, make this a theme of major interest for multi-messenger astrophysics. This review discusses the future facilities and observational strategies that are likely to significantly advance this fascinating field.

Adding VLBI capability to the SKA arrays will greatly broaden the science of the SKA, and is feasible within the current specifications. SKA-VLBI can be initially implemented by providing phased-array outputs for SKA1-MID and SKA1-SUR and using these extremely sensitive stations with other radio telescopes, and in SKA2 by realising a distributed configuration providing baselines up to thousands of km, merging it with existing VLBI networks. The motivation for and the possible realization of SKA-VLBI is described in this paper.Advancing Astrophysics with the Square Kilometre Array

High-resolution observations of high-redshift (z > 4) radio quasars offer a unique insight into jet kinematics at early cosmological epochs, as well as constraints on cosmological model parameters. Due to the general weakness of extremely distant objects and the apparently slow structural changes caused by cosmological time dilation, only a couple of high-redshift quasars have been studied with parsec-scale resolutions, and with limited number of observing epochs. Here we report on very long baseline interferometry (VLBI) observations of a high-redshift blazar J1430+4204 (z = 4.72) in the 8 GHz frequency band at five different epochs spanning 22 years. The source shows a compact core-jet structure with two jet components being identified within 3 milli-arcsecond (mas) scale. The long time span and multiple-epoch data allow for the kinematic studies of the jet components. That results in a jet proper motion of µ(J1) = 0.017±0.002 mas yr −1 and µ(J2)=0.156±0.015 mas yr −1 , respectively. For the fastestmoving outer jet component J2, the corresponding apparent transverse speed is 19.5 ± 1.9 c. The inferred bulk jet Lorentz factor Γ = 14.6 ± 3.8 and viewing angle θ = 2.2 • ± 1.6 • indicate highly relativistic beaming. The Lorentz factor and apparent proper motion are the highest measured to date among the z > 4 jetted radio sources, while the jet kinematics is still consistent with the cosmological interpretation of quasar redshifts.