Abstract:
Gravitational lensing and gravitational wave are two important predictions of Einstein’s theory of general relativity. Gravitational lensing has become a powerful astrophysical tool with rich astronomical observations, while the direct detection of gravitational waves has opened a brand-new window to explore the Universe. This paper presents the significance of lensed gravitational waves in astronomy, with particular emphasis on gravitational wave lensing phenomena and their distinctive applications in modern cosmology. Firstly, we review the theoretical framework and observational history of electromagnetic gravitational lensing, followed by a detailed discussion of the unique characteristics of gravitational wave lensing, including its high-precision time delay measurements and the intricate modulation patterns induced by wave optics effects. Secondly, three methods for identifying lensed gravitational wave signals are also detaildly outlined, with their application in dark matter and its substructure detection, Hubble constant measurement, and tests of dark energy and modified gravity theories. Finally, we emphasize the crucial role of future ground and space-based gravitational wave detectors, with the expectation that lensed gravitational waves will serve as a indispensable and powerful tool in modern cosmology.