Cosmic strings (CS) are one-dimensional cosmological-size objects predicted in realistic models of the early Universe. Analysis of the cosmic microwave background (CMB) anisotropy data from the Wilkinson Microwave Anisotropy Probe (WMAP) and Planck surveys revealed several CS candidates. One of the candidates, CSc-1, was found to be most reliable because of the statistically significant chains of gravitational lensing (GL) candidates in its field. We observed the brightest of the objects in the CSc-1 field, a galaxy pair SDSSJ110429.61+233150.3. The significant correlation between the spectra of the two components indicates the possible GL nature of the pair. Our simulations of observational data in the CSc-1 field shows that a large number of pairs can be explained by the complex geometry of the CS. Simulations of the SDSSJ110429 galaxy pair has shown that the observed angle between the components of the pair can be explained if the CS is strongly inclined and, possibly, bent in the image plane. In our preliminary data, we also detected the sign of the sharp isophotal edge in one image, which along with CMB and spectral data strongly suggests the possibility of a CS detection.

It is discussed in detail the complete mathematical model of gravitational lensing on a single cosmic string (CS) of general shape and position with respect to the line of sight. CS are one-dimensional extended objects assuredly predicted by modern cosmology. The presence of CS changes the global geometry of the Universe, could clarify the properties of the early Universe, including inflation models, and could serve as a unique proof of higher-dimensional theories. Despite the fact that CS have not yet been reliable detected, there are several strong independent indications of the existence of the CS, based of CMB analysis and search of gravitational lens chains with special properties (The recent new indication of the existence of the CSs is the nHz gravitational waves in the NANOGrav and other PTA Collaborations data.) However, early considered models of straight CS presented only a small fraction of the general CS-configurations to be observed. Now we propose model which could significantly increase the possibilities of CS observational search. It is considered more realistic models have necessarily include the inclinations and bends of the CS. Besides, the recent analysis of observational data on the search for gravitational-lens candidates, shows a large number of pairs that could be explained by the complex geometry of the CS.

The structure of spacetime near a wormhole (WH) and possible observational consequences are investigated theoretically. In connection with the growing accuracy of observations and the prospects of a new gravitational-wave channel, the problem of distinguishing between astrophysical manifestations of black holes (BHs) and hypothetical WHs is becoming relevant. WHs, along with BHs, naturally arise within general relativity (GR). Observational searches for WHs require knowledge of the characteristic trajectories of bodies in its vicinity, including the trajectories entering its throat. Equations of motion of a test particle in the WH metric are derived, and the most interesting properties of these motions are considered. A general equation of geodesics in the WH metric is derived, and some properties of these geodesics are considered. The exact solution for circular orbits of test particles around a WH, as well as an approximate analytical solution of the geodesic equations, is analyzed. The shift of the pericenter of the orbit of a test particle in the WH field is considered, and possible observational consequences are discussed. Examples of test particle trajectories near a WH are presented that are obtained by numerical simulation.

The paper develops a method for detecting optical binary stars based on the use of astrometric catalogs in combination with machine learning (ML) methods. A computational experiment was carried out on the example of the HIPPARCOS mission catalog and the Pan-STARRS (PS1) catalog by applying the suggested method. It has shown that the reliability of predicting a stellar binarity reaches 90-95 proprietary research platform - Cognotron.

The principles and technical requirements for using the classical Michelson interferometer as a rangefinder in a constellation of satellites for measuring the parameters of the Earth's gravitational field are considered.

The paper consistently presents the history and methodology of observational searches for cosmic strings of various nature. Cosmic strings are one-dimensional extended objects predicted by modern cosmology, which, however, have not yet been detected with a high degree of confidence. The presence of cosmic strings changes the global geometry of the Universe and could serve as a unique proof of higher-dimensional theories. The properties and features of these cosmological objects from the point of view of observational astronomy are discussed. The presentation is preceded by a brief mathematical theory of cosmic strings.

Nonstandard techniques to deliver a payload from the Moon to Earth are explored. Two approaches are compared, which are based on using a space elevator and an acceleration device, the Artsimovich railgun. The energy needed to launch a payload to a low lunar orbit and the L_1 libration point in the Earth–Moon system is estimated. We conclude that the railgun is economically advantageous compared to the space elevator and standard jet technologies.

A near-Earth gravity experiment is considered in which a pair of satellites exchange laser signals. As a concrete example, numerical estimates were made using the satellite configuration in the GRACE-FO mission. An expression for the signal phase is obtained, which provides an accuracy of 1 picometer (pm) when calculating the distance between satellites. The influence of all significant gravitational effects on the signal propagation, such as the gravimagnetic field of the Earth and the tidal fields of the Sun and Moon, is considered. Special attention is paid to the study of the contributions of the Earth's potential harmonics. Phase perturbations of the first and second orders are considered, and it is shown that the effect of the second-order corrections lies beyond the accuracy of 1 pm. This makes it possible to express the signal phase in a fairly compact form.

The paper considers the principles of space navigation using pulsars observed in the radio range. The requirements for receiving equipment are outlined, a recommended pulsar list is given, and an algorithm for determining the position of a spacecraft in barycentric coordinates and calculating corrections to the onboard time scale is described.

— The theory of relativistic reductions for future challenges of space gravimetry with target accuracy of up to 1 picometer is developed in this paper.

The advancement of space technology opens new perspectives in developing high-resolution models of the Earth’s gravitational field. The use of a precision laser interferometric system requires taking relativistic effects in the inter-satellite ranging within the satellite constellation into account. The main quantity measured by the laser system is the phase incursion of the laser beam when passing a double one-way range between the satellites. A solution for the relativistic phase is obtained that considers not only the usual Shapiro term but also the contribution of the quadrupole term to distributions of the Earth’s mass, the Earth’s spin, and tidal gravitational fields caused by the gravitational potentials of the outer bodies of the Solar System. Relativistic reduction terms are estimated at the accuracy level of ∼1 nm, which fully satisfies the accuracy of precision measurements in the two-spacecraft formation. It will be necessary to take the relativistic effects of the next order of smallness into account in the next-generation gravitational twin missions.

The complexity of the cosmological scenario regarding cosmic strings (CSs) stands still in the way of a complete understanding. We describe here a promising strategy for the possible detection of these elusive physical entities. It is based on the search of strong gravitational lensing events in the location area of the CS candidate (CSc-1), which was declared in a previous work by CMB analysis. Using photometric and geometric criteria, we identified pairs of candidates of lensed galaxies (LGCs) in the "string field" (SF), which were then compared with the average density of background galaxy pairs in a set of "control fields" (CFs). We found an excess of $22\%$ (per sq. deg.) of the LGCs in SF, which exceeds the estimated cosmic dispersion. We also found that the number of LGCs is in excess of $29.2\%$ in the angular separation bin $[8'', 9'']$. Finally, we analysed the possibility of a preferred orientation of the line connecting the centres of the LGCs. The orientation is statistically significant for an angular separation bin $[4'',6'']$. Therefore, we found two "windows" for the preferred angular separation for LGCs along the possible CS. However, the confirmation of the gravitational lensing origin of our LGCs requires spectroscopic observations which seem to be justified by the present results. We plan to acquire their spectra as well as to continue the study of the spectral and morphological features of the LGCs in the CSc-1 field and to analyse the other CS-candidates using the same strategy.

A pulsar time scale is considered, including possibilities for its realization and possible applications to fundamental problems in astronomy and physics.

This review considers the problem of autonomously determining the position of a spacecraft in space based on the analysis of pulses emitted by X-ray pulsars. The characteristics of the prospective equipment and lists of pulsar candidates for reference sources are given. The navigation algorithm and resulting accuracy characteristics are substantiated.