Flatness problem

The flatness problem is the puzzle of why the universe’s spatial curvature is so close to zero, even though standard cosmological expansion makes deviations from flatness grow over time.

Friedmann equations: Equations of general relativity that relate cosmic expansion to matter, radiation, curvature, and the cosmological constant. They show why the density required for flatness changes as the universe expands.
Alexander Friedmann: A Russian mathematician who derived expanding and contracting cosmological solutions to general relativity. His equations made the evolution of spatial curvature part of modern cosmology.
General relativity: Einstein’s theory of gravity, in which matter and energy shape spacetime geometry. Cosmological curvature and expansion follow from applying this theory to the universe.
Big Bang cosmology: The account of an expanding universe that evolved from an early hot, dense state. Without an added mechanism such as inflation, its standard expansion leaves the flatness puzzle.
Horizon problem: The puzzle of why widely separated regions of the universe have nearly identical properties despite limited causal contact. It is a second initial-condition puzzle that inflation was designed to address alongside flatness.
Critical density: The cosmic mass-energy density that makes spatial geometry flat in the standard Friedmann model. The problem asks why the actual density remains so close to this threshold.
Georges Lemaître: A Belgian priest and physicist who developed an expanding-universe model and proposed a primeval atom. His early-universe cosmology helped frame questions about the universe’s initial conditions.
Friedmann–Lemaître–Robertson–Walker metric: A spacetime geometry describing a homogeneous and isotropic expanding or contracting universe. It separates spatial curvature from the universe’s changing scale factor.
Eternal inflation: A class of inflationary models in which inflation continues in some regions while ending in others. It extends inflation’s account of flatness into a picture of many causally separate regions.
Cosmological constant problem: The discrepancy between the observed vacuum energy density and quantum-field estimates of its natural scale. Like flatness, it exposes a mismatch between cosmological observations and expectations about fundamental physics.

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