Enhancing the potential of gravitational waves as standard sirens: a statistical analysis

The discovery of gravitational waves (GWs) from compact binary coalescences in 2015 unlocked new possibilities for studying the Universe. As their intrinsic loudness can be predicted by General Relativity, GWs provide a direct measurement of the luminosity distance, making them standard sirens. To complement this information and use them as cosmological probes, it is necessary to break the degeneracy between the redshift and the binary masses. In the absence of an electromagnetic counterpart, galaxy catalogues can be used to break this degeneracy, and in this case GWs are referred to as dark sirens. In this Thesis, I used GW events as dark sirens to constrain parameters of different binary black hole mass function (MF) models. I investigated two mock GW catalogues simulating the current O4 and future O5 observing runs by the LIGO-Virgo-KAGRA network, and explored the capability of discriminating between the different MF models with future data. I implemented a new MF model and a nested sampling-based posterior sampling method in the CHIMERA code to estimate Bayesian evidence of different MFs. In addition, I developed code to compute statistical diagnostics such as logB, DIC, and PPC for model selection. Analysing the GW catalogues with available MFs, I constrained their parameters, compared them, and identified the best-fitting model along with the capability to distinguish them. Simultaneously, I conducted a sizing analysis to estimate computational time for GW data analysis. In the last part, I investigated the potential effects of different catalogue assumptions on results, including errors in galaxy catalogue redshift, GW event data smoothing methods, and varying GW event samples. This work paves the way for the optimisation of future GW analysis, proposing strategies to maximise the scientific return and computing capabilities and providing forecasts on expected performances achievable with future GW data.