FriedmannLemaîtreRobertsonWalkerSchema

Friedmann-Lemaître–Robertson–Walker (FLRW) cosmology refers to a family of solutions to Einstein's field equations that assume the universe is homogeneous and isotropic on large scales. The spacetime metric describes a universe with a time-dependent scale factor a(t) that encodes expansion or contraction, and a constant spatial curvature parameter k that can be -1, 0, or +1.

The dynamics are governed by the Friedmann equations, derived from the Einstein equations for a perfect fluid with energy density ρ and pressure p. With the Hubble parameter H = ȧ/a, they take the form: H^2 = (8πG/3)ρ - kc^2/a^2 + Λ/3, and ä/a = -(4πG/3)(ρ+3p/c^2) + Λ/3. A conservation equation ρ̇ + 3H(ρ+p) = 0 also applies. Different components, such as matter, radiation, and dark energy, evolve differently as the scale factor changes.

History and naming reflect contributions from multiple scientists. Alexander Friedmann showed in the 1920s that general relativity allows dynamic universes that expand or contract. Georges Lemaître, in 1927, independently derived expanding solutions and linked them to observed galactic redshifts, proposing the primeval-atom concept. The Robertson–Walker form was developed by Howard P. Robertson and Arthur G. Walker in the 1930s, yielding the widely used metric that bears their names in modern cosmology.

Impact: The FLRW framework underpins the standard model of cosmology, including the ΛCDM paradigm. It supports the observed expansion, cosmic microwave background, and large-scale structure, while encoding geometry and late-time acceleration through k and the cosmological constant Λ.