Problems and methods of modern search for cosmic strings

The paper considers a generalized model of gravitational lensing (GL) of background objects (galaxies) on cosmic strings (CS). CS are essentially one-dimensional objects of cosmological scales, which can have both a topological nature and be the consequences of interactions of multidimensional spaces in the early pre-inflationary Universe. CS have not been reliably detected at the current moment. The method of searching for special GL events is one of the key methods of searching for such objects. The paper discusses lensing on CS of a general position, including those with a significant inclination relative to the line of sight connecting the observer and the background object, as well as those with a curvature in the plane perpendicular to the line of sight. Based on the modeling, it is concluded that the strategy of searching for chains of GL events can be revised in favor of searching for clusters of such GL events. The influence of CS geometry on the number of GL events is also discussed: for example, with a sufficiently large curvature, GL pairs do not form. The simulation results are confirmed by observational data. The possibility of the existence of CS with significantly higher tensions than is traditionally considered in the framework of the CS network model is also indicated.