Gravitational Wave Cosmology

Since their first detection in 2015, gravitational wave observations have enabled a variety of studies, ranging from stellar evolution to fundamental physics. In this chapter, we focus on their use as "standard sirens", describing the different methodologies that can be adopted to measure cosmological parameters with compact object binaries from ground-based gravitational wave detectors. We cover the three main classes of standard siren measurements, showing how the expansion of the Universe can be constrained through Bayesian statistics both with gravitational wave observations alone and with the aid of electromagnetic emission from the electromagnetic counterpart of gravitational wave events and from galaxies. Finally, we summarize the existing measurements and prospects for future constraints on cosmological parameters.