Detecting Gravitational Waves with Time-dependent Lensing Reconstruction

Gravitational waves (GWs) have emerged as a powerful tool for probing the universe, complementing traditional light-based observations and inspiring the development of new detection instruments. My aim is to introduce a new technique to detect GWs in a broad range of frequencies using existing and future cosmological surveys. As GWs pass through Earth, they causes a deflections of the incoming light in a similar manner found in gravitational lensing. This document proposes the development of a new time-varying lensing reconstruction enabling us to forecast the sensitivity of our new technique. While this technique may not match the sensitivity of Pulsar Timing Arrays (PTAs) within their specific frequency range, it holds the potential to place constraints on sub-nanohertz GWs.