The Einstein Equivalence Principle (EEP) is a cornerstone of general relativity and predicts the existence of gravitational redshift. We report on new results of measuring this shift with RadioAstron (RA), a space very long baseline interferometry (VLBI) spacecraft launched into an evolving high eccentricity orbit around Earth with geocentric distances reaching 353 000 km. The spacecraft and ground tracking stations at Pushchino, Russia, and Green Bank, USA, were each equipped with a hydrogen maser frequency standard allowing a possible violation of the predicted gravitational redshift, in the form of a violation parameter ɛ, to be measured. By alternating between RA’s frequency referencing modes during dedicated sessions between 2015 and 2017, the recorded downlink frequencies can essentially be corrected for the non-relativistic Doppler shift. We report on an analysis using the Doppler-tracking frequency measurements made during these sessions and find ε = ( 2.1 ± 3.3 ) × 10 − 4 . We also discuss prospects for measuring ɛ with a significantly smaller uncertainty using instead the time-domain recordings of the spacecraft signals and envision how 10⁻⁷ might be possible for a future space VLBI mission.

In this paper, we estimate efficiency of a conceivable Euro-Asian network of gravitational wave (GW) interferometers that might be realized having in mind a plan of construction of third generation interferometer in Novosibirsk region. Subsequently, some network would be composed, including four GW detectors. Among them there are the already active interferometers VIRGO (Italy) and KAGRA (Japan), Indian interferometer under construction—LIGO India and the interferometer in Siberia mentioned above. The quality of network in question is considered on the base of typical numerical criteria of efficiency for detecting GW signals of known structure—radiation of relativistic binary coalescence.

A special class of solutions of the equations of cosmological dynamics implying analytic connection between inflationary models in the framework of general relativity and Einstein–Gauss–Bonnet gravity is considered. The possibility of verification of such models by direct observation of relic gravitational waves, the spectrum of which is determined by the parameters of the model was analyzed.

An approach to construct cosmological inflation models on the basis of a certain dependence of the scalar field evolution on the e-folds number is considered. The reconstruction of the model background parameters according to the kind of specific connection between the parameters of cosmological perturbations is proposed. By the slow-roll approximation, as functions of the e-fold number, the scalar field potential and the Hubble parameter are determined. The logarithmic dependence between the scalar field evolution and the number of e-folds is investigated as the example. The derived model was found to obey a quadratic law between the parameters of cosmological perturbations. On the basis of suggested approach, a new cosmological inflation model with an exponential potential is proposed. This complies with existing observational constraints for both background and perturbation spectrum parameters. A comparison of obtained results with the solutions obtained by the symbol regression is made. The restrictions for arbitrary parameters in the model with logarithmic potential are also considered. The proposed form of the scalar field potential is consistent with one of the optimal potentials obtained when using machine learning methods to analyze the correspondence of inflationary models to observational data and gravitational waves contribution to the anisotropy and polarization of the CMB.