Focus Point on Tensions in Cosmology from Early to Late Universe: Part II: New Directions in the Light of Observations from the Most Modern Astronomical Facilities

The papers included in this Focus Point collection are devoted to the studies on the cosmological tensions and challenges stimulated by the latest observational data. The first results of the LARES-2 laser ranging satellite on the high precision testing of the frame-dragging effect predicted by General Relativity are presented. The data on the S-stars monitoring in the Galactic center obtained by GRAVITY collaboration were analysed within the Physics-informed neural network (PINN) approach. The results enabled to probe the role of the cosmological constant, of the dark matter, the star cluster in the core of the Galaxy obtaining an upper limit for the star density. The topics include the conversion of high-frequency relic gravitational waves into photons in cosmological magnetic field, cosmological gravitational waves stochastic background generation through the spontaneous breaking of a global baryon number symmetry, observational predictions of the Starobinsky inflation model and other studies.