Exploring the uncharted Universe with Gravitational Waves

Gravitational waves (GW) emitted by compact binary coalescences are natural cosmological probes. These 'standard siren' sources offer direct measurements of the luminosity distance across the cosmic history. Features in the mass distribution, such as bumps and dips, undergo redshift and thus provide statistical constraints on the redshift distribution of the population, allowing for measurements of the Universe’s expansion. At the same time, GWs originating from high-redshift events could be gravitationally lensed, offering a unique way to map the matter distribution in the Universe. In this talk, I will explore the utilization of the mass spectrum of neutron stars and black holes in GW compact binaries to probe the standard cosmological model. I will demonstrate the potential of these 'spectral sirens' in constraining the high-redshift expansion rate and testing gravity. Additionally, I will discuss the prospects and challenges associated with identifying lensed GW events using current ground-based detectors like LIGO-Virgo-KAGRA and future space-based antennas such as LISA.