The recent discovery of gravitational waves has opened unprecedented avenues to the frontiers of science. This project would focus on the extraction of science results, cosmology and fundamental physics in particular, with observational data from the upcoming observing runs of the LIGO-Virgo-KAGRA detector network. Some of the big questions that this project aims to understand are: (i) How fast is the universe expanding? (ii) Are the gravitational-wave observations consistent with Einstein’s general relativity? (iii) Can gravitational-waves tell us about the structure of matter at the largest scales in the universe? This research will also pave the way to observational science with the next generation of gravitational-wave detectors including the Einstein Telescope and broaden the field of gravitational-wave science beyond its current horizons.