Friedmann equations

The Friedmann equations describe how the scale factor of a homogeneous, isotropic universe evolves under general relativity, depending on its contents, spatial curvature, and cosmological constant.

Scale factor: A time-dependent measure of how distances between comoving points change in an expanding or contracting universe. Its time evolution is the central quantity governed by the equations.
General relativity: Einstein’s theory of gravity, in which spacetime geometry is shaped by energy and momentum. The Friedmann equations are a symmetry-reduced form of its field equations.
Lambda-CDM model: The standard cosmological model, combining a cosmological constant with cold dark matter and ordinary matter. Its expansion history is calculated by solving the Friedmann equations for these components.
Alexander Friedmann: A Russian mathematician and physicist who derived dynamic, nonstatic cosmological solutions to general relativity. His 1922 and 1924 papers established the equations’ original solutions.
Hubble parameter: The fractional rate of change of the cosmological scale factor with time. It expresses the expansion rate appearing in the first Friedmann equation.
Einstein field equations: Tensor equations relating spacetime curvature to the energy and momentum of matter and fields. Imposing cosmic homogeneity and isotropy on these equations yields the Friedmann equations.
Big Bang nucleosynthesis: The early-universe production of light atomic nuclei during the first minutes after the Big Bang. The expansion rate from these equations controls how long nuclear reactions can proceed.
Georges Lemaître: A Belgian priest and physicist who developed an expanding-universe model and linked it to astronomical observations. His independent work connected relativistic expansion equations with an expanding cosmos.
Energy density: The amount of energy contained per unit volume in a physical system. Cosmic energy density contributes directly to the expansion rate.
Friedmann–Lemaître–Robertson–Walker metric: A spacetime metric describing a homogeneous, isotropic universe with time-dependent scale factor. This metric supplies the geometry assumed in their derivation.

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