Cosmology with gravitational waves: Inferring the Hubble constant with standard sirens

The following proceeding aims to provide an overview of the discussion presented at the 20th edition of “Incontri di Fisica delle Alte Energie” (IFAE) held in Florence from 3 to 5 April 2024. We will delve into some of the principal cosmological inference methods currently available using gravitational waves detected by the LIGO, Virgo, and KAGRA interferometers. Our focus will be the Hubble constant estimation with standard sirens, thus called gravitational wave detections, which have the property to provide directly the source’s luminosity distance. The use of sirens for cosmological studies had been proposed long before the first gravitational wave detection by B. Schutz and has been further developed within the Bayesian framework by several authors. In particular, the following proceeding will provide a brief description of the bright siren method, the spectral siren method, and how to measure the Hubble constant with the support of the galaxy catalogue information. These new statistical approaches show potential with the first published data, offering only a glimpse of the precision and accuracy achievable in the coming years with third-generation interferometers and increasingly accurate galaxy redshift measurements.