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Explore the fundamentals of gravitational wave cosmology in this comprehensive lecture delivered as part of the V Joint ICTP-Trieste/ICTP-SAIFR School on Cosmology. Delve into advanced concepts and theoretical frameworks that connect gravitational wave observations to cosmological phenomena, building upon foundational knowledge from previous sessions. Learn how gravitational waves serve as powerful probes for understanding the universe's structure, evolution, and fundamental physics. Examine the latest developments in gravitational wave detection and their implications for cosmological research, including insights into dark matter, dark energy, and the early universe. Discover how these ripples in spacetime provide unique windows into cosmic events and processes that are otherwise inaccessible through traditional electromagnetic observations. Gain understanding of the mathematical formalism and observational techniques used to extract cosmological information from gravitational wave data, and explore the synergies between gravitational wave astronomy and other cosmological probes.
