Cosmological Gravitational Waves in the Wave-Optics Limit

Gravitational lensing of waves is an intriguing phenomenon that highlights the complex interaction between the properties of the wave and the geometry of the lens. The lensing behavior is strongly influenced by the relative length scales: when the wavelength of the wave approaches the Schwarzschild radius of the lens, wave-like effects such as interference, diffraction, and polarization shifts become prominent. These effects significantly alter the waveforms, introducing intricate modifications that cannot be explained by classical ray-based methods. In this thesis, we expand upon the latest formalism developed to account for these wave effects, which is based on the proper-time technique. We investigate the potential of this approach in a cosmological setting, addressing more general scenarios involving multiple lenses and sources, and incorporating the effects of the Universe’s expansion.