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Explore the application of gravitational wave standard sirens for cosmological distance measurements in this lecture from the Summer School on Gravitational-Wave Astronomy. Learn how gravitational wave detections can serve as "standard sirens" - analogous to standard candles in optical astronomy - to measure cosmic distances and probe the expansion history of the universe. Discover the theoretical foundations of using binary neutron star and black hole mergers as cosmological probes, understand the methodology for extracting distance information from gravitational wave signals, and examine how these measurements complement traditional cosmological observations. Investigate the potential of multi-messenger astronomy, where gravitational wave detections are combined with electromagnetic counterparts to provide independent constraints on cosmological parameters such as the Hubble constant. Analyze current results from LIGO-Virgo observations and their implications for cosmology, while exploring future prospects with next-generation gravitational wave detectors. Gain insights into the systematic uncertainties, selection effects, and statistical methods involved in cosmographic studies using gravitational wave standard sirens, and understand how this emerging field contributes to precision cosmology and our understanding of dark energy and the cosmic expansion rate.
