Gravity at extremes From black holes to cosmology

Gravity is a fundamental force shaping the universe across scales, as described by Albert Einstein's theory of general relativity. While general relativity adeptly explains celestial motion and structure formation in weak gravitational fields, it encounters challenges in the quantum realm and the dark sector of cosmology. The advent of gravitational wave astronomy in 2015 has enabled precision tests of gravity in strong-field and dynamic environments, such as around black holes and neutron stars, and has inspired new approaches to cosmology. This thesis advances tests of gravity in two distinct areas: examining strong-field deviations from general relativity using gravitational waves and determining the cosmological expansion rate with state-of-the-art measurement techniques.
In this context, Part I focuses on deriving analytical waveforms for binary black holes within the scalar-Gauss-Bonnet (sGB) class of theories, which extend general relativity through non-linear curvature terms coupled to a scalar field. Part II explores two novel strategies for measuring cosmological parameters: using gravitational waves as standard sirens and analyzing strongly lensed electromagnetic observations of massive objects like quasars.