Gravitational wave cosmology: measuring the Hubble constant with dark standard sirens

The fact that the universe is expanding has long been agreed upon, but the rate at which it is doing so, the Hubble constant, is a cause of disagreement across the field of cosmology, with a tension between early- and late-time measurements that could either be due to systematic measurement uncertainty, or an as-yet unknown discrepancy between the cosmological model and our universe. The use of gravitational wave standard sirens for cosmological measurements has long been considered. Gravitational wave signals from compact binary coalescences have their distance encoded within them, and require no other form of calibration, making them independent of the cosmic distance ladder. A measurement of the Hubble constant using standard sirens would, by agreeing with the early-time or late-time measurements, give an indication as to whether the solution to the Hubble constant tension is systematic error or exciting new physics. The detection of the binary neutron star merger, GW170817, alongside its electromagnetic counterpart, gave rise to the first measurement of the Hubble constant using gravitational waves. Further gravitational wave detections are required in order to improve the precision enough to discriminate between the early- and late-time Hubble constant measurements, but as of 2021 no other gravitational wave detections have been linked unambiguously with an electromagnetic counterpart. In 1986, Schutz proposed a method for measuring the Hubble constant using gravitational wave detections when observed without electromagnetic counterparts (hence the term dark stan- dard sirens). Galaxy catalogues can be used instead to provide the redshifts of potential host galaxies, and the uncertainty of which galaxy is the real host can be marginalised over. This thesis takes Schutz’s original proposition and places it in a Bayesian framework which allows the incompleteness of the galaxy catalogue (and the possibility that the host galaxy of a gravitational wave event won’t be contained within it) to be accounted for. Gravitational wave selection effects (due to the finite sensitivity of the current detectors) are also incorporated into the methodology. This methodology is implemented in a software package, gwcosmo, which is then tested using a series of mock data analyses of increasing complexity. Following the success of this, the gravitational wave detections from Advanced LIGO and Virgo’s first and second observing runs are used, in combination with publicly available galaxy catalogues, to make the first measurement of the Hubble constant that combines data from multiple gravitational wave detections. Finally, further improvements are made to gwcosmo that take into account variations in the completeness of galaxy catalogues across the sky. This work paves the way for the analysis of the gravitational wave data from Advanced LIGO and Virgo’s third observing run, and beyond