Probing modified Gravitational Wave propagation using Standard Sirens with future observational data

Gravitational waves (GWs) are writing a new chapter in cosmology as novel and independent probes to measure the expansion history and test the foundations of gravitational physics. In particular, GWs directly provide the luminosity distance to their source, bypassing the uncertainties of traditional distance ladders. However, this distance may differ from the electromagnetic one, due to modified GW propagation predicted by various modified gravity (MG) theories. This thesis explores the potential of future GW observations to constrain modified GW propagation and potential biases on H0. We use CHIMERA, a pipeline for joint inference of cosmological and astrophysical population parameters that we extended to include MG effects with the (Ξ0, n), parametrization. We generate GW catalogs assuming MG cosmologies and simulate their observation with the configuration of the future LIGO Virgo KAGRA observing run (O5). After exploring potential systematics in one-dimensional posteriors, we run full Markov chain Monte Carlo (MCMC) analyses including a galaxy catalog with spectroscopic redshift measurements, and derive constraints on both cosmological and MG parameters. We find a significant correlation between H0 and Ξ0 due to their relationship with luminosity distance at fixed z. By fixing H0 to the fiducial value, we recover Ξ0 with an uncertainty of 3%. On the other hand, if Ξ0 is fixed, H0 is constrained at 1% in a GR universe (Ξ0 = 1), 1.2%, and 2% in different MG universe with Ξ0 = 1.8 and 0.6, respectively. In a full MCMC analysis, when both H0 and Ξ0 vary, their inherent degeneracy leads to weaker constraints, finding 2.3%, 6% and 7% for H0 while 10%, 17% and 20% for Ξ0, respectively for the different cosmologies. This work provides a first assessment of the constraints that can be achieved on those parameters with future GW data, paving the way to properly model them to derive unbiased and precise determinations of cosmological parameters.