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Explore advanced concepts in gravitational wave cosmology through this comprehensive lecture delivered at the Graduate School "ISAPP2025: Gravitational Waves: From Theory to Detection" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the theoretical foundations and practical applications of gravitational waves in cosmological contexts, building upon fundamental principles to examine how these ripples in spacetime provide unique insights into the structure and evolution of the universe. Learn about the intersection of general relativity, cosmology, and gravitational wave physics, including topics such as primordial gravitational waves, their role as probes of the early universe, and their significance in understanding cosmic inflation and other cosmological phenomena. Gain expertise in the mathematical frameworks used to describe gravitational wave propagation in cosmological backgrounds and discover how these waves serve as powerful tools for testing cosmological models and extracting information about the universe's history and composition.
