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This thesis explores the fields of gravitational waves, cosmology, and fundamental physics, focusing on how gravitational waves can help us unlock the mysteries of the Universe. These waves (ripples in the fabric of spacetime) originate from highly energetic events during the Universe’s history and offer a powerful new tool for discovery. This work examines both the challenges and opportunities involved in extracting cosmological and astrophysical information from gravitational wave signals.

Maximizing the scientific impact of gravitational wave observations requires precise theoretical predictions to guide experimental searches and enable meaningful data comparisons. To this end, one focus of this thesis is on theoretical aspects of the quantum effective action, a tool that accounts for quantum effects in physical systems. The calculations developed have broad applications in cosmology, particularly in improving predictions of gravitational waves from the early Universe.

The second key topic of this thesis is gravitational lensing (the bending of gravitational waves caused by massive objects) and its impact on the measurement of astrophysical and cosmological parameters. Working in the context of future gravitational wave experiments, we show that accounting for lensing is of paramount importance in order to obtain correct information from gravitational wave data.

Overall, this thesis contributes to the development of rigorous methodologies for addressing key cosmological puzzles using gravitational wave. By producing accurate theoretical predictions, this work strengthens the foundation of gravitational wave cosmology and contributes toward a better understanding of our Universe through this emerging observational window.