The Lilly–Madau plot serves as a vital cosmological diagram tracing the star-formation rate density of the universe across billions of years. We examine the classic model of cosmic history, which depicts star formation rising to a peak at redshift z≈2 before declining toward the present day. While modern data from the James Webb Space Telescope confirms this general shape, it reveals that star formation in the early universe was more intense and began sooner than previously expected. Conversely, studies of the Local Cosmological Volume show that nearby galaxies have maintained relatively constant star-formation rates that do not match the dramatic global peak. This discrepancy suggests the possibility of large-scale matter inhomogeneities or a local underdensity that challenges the assumption of a perfectly uniform universe. Ultimately, the sources use the Lilly–Madau framework to bridge our understanding of galaxy evolution, black hole growth, and the timing of cosmic reionization.

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