Near Flat Curvature

Observations of the Cosmic Microwave Background and large-scale structure indicate that the geometry of the observable universe is spatially flat to within a margin of error of about 0.4% ($\Omega_k \approx 0$). In the standard Big Bang model without inflation, this near-flatness is a fine-tuning problem known as the "flatness problem," because any deviation from perfect flatness in the early universe would grow rapidly over time. The observed flatness requires the initial density to be tuned to the critical density with extreme precision, a coincidence that Lambda-CDM solves by invoking a period of exponential inflation, although the mechanism for starting and stopping inflation introduces its own theoretical challenges (Guth 1981; Planck Collaboration 2020).

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