Executive Summary : | Gravitational lensing of gravitational-waves (GWs) from compact binary coalescences (CBCs) and the accelerated motion of CBCs are two of the most anticipated discoveries in GW astronomy. The LIGO-Virgo-Kagra's 4th observing run is set to start in May 2023 and last for about 1.5 years. It is crucial to develop tools to enable these discoveries and their astrophysical implications. A rapid and interpretable chi-square statistic will be developed to assess if two temporally resolved GW signals in detector data have identical phase morphology, indicating that both signals originate from the same source and were strongly lensed by a galaxy or cluster. This statistic will be used to search for strongly lensed GW event pairs in publicly available LIGO-Virgo detector data. The researchers also propose to leverage strong lensing of GWs from CBCs with electromagnetic counterparts to enhance multi-messenger astronomy. If the CBC is lensed, its host galaxy must also be lensed. Tools to accurately extract image time-delays from lensed images of host galaxies will be developed, and the resolution required to make time-delay predictions will be assessed. For the detection and interpretation of accelerated motion of CBCs, GW templates incorporating corrections due to accelerated motion will be developed. These constraints can be interpreted in the context of mergers around supermassive black holes (SMBHs), yielding estimates of the rates of these mergers in their vicinity. |