Combining gravitational and electromagnetic waves observations to investigate the Hubble tension

Recent estimations of the Hubble parameter $H_0$ based on gravitational waves (GW) observations can be used to shed some light on the discrepancy between the value of the Hubble parameter $H_0^P$ obtained from large scale observations such as the Planck mission, and the small scale value $H_0^R$, obtained from low redshift supernovae (SNe). In order to investigate the origin of this discrepancy we perform a combined analysis of the luminosity distance of SNe and GW sources, using different methods, finding that the impact of the GW data is very limited, due to the small number of data points, and their large errors. We analyze separately data from the Pantheon and the Union 2.1 catalogues, finding that a model with $H_0^P$ and a small local void can fit the data as well as a homogeneous model with $H_0^R$, resolving the apparent $H_0$ tension. We find that there is a significant difference between the size and depth of the inhomogeneity obtained using the two datasets, which could be due to the different sky coverage of the two catalogues. For Pantheon we obtain evidence of a local inhomogeneity with a density contrast $\delta_v=-0.155 \pm 0.026$, extending up to a redshift of $z_v = 0.056 \pm 0.0002$, while for Union 2.1 we obtain $\delta_v=-0.461 \pm 0.032$ and $z_v= 0.081\pm 0.008$. We also perform some analysis using redshift shell averaged data, and obtain approximately the same results, hinting to the fact that the effects of the monopole component of the local inhomogeneity are the dominant ones