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Astronomy portal. v. t. e. The Friedmann–Lemaître–Robertson–Walker metric (FLRW; / ˈfriːdmən ləˈmɛtrə ... /) is a metric based on an exact solution of the Einstein field equations of general relativity. The metric describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe that is path-connected, but not ...
They were first derived by Alexander Friedmann in 1922 from Einstein's field equations of gravitation for the Friedmann–Lemaître–Robertson–Walker metric and a perfect fluid with a given mass density ρ and pressure p. [1] The equations for negative spatial curvature were given by Friedmann in 1924. [2]
Scale factor (cosmology) The expansion of the universe is parametrized by a dimensionless scale factor . Also known as the cosmic scale factor or sometimes the Robertson–Walker scale factor, [1] this is a key parameter of the Friedmann equations. In the early stages of the Big Bang, most of the energy was in the form of radiation, and that ...
The equation of state may be used in Friedmann–Lemaître–Robertson–Walker (FLRW) equations to describe the evolution of an isotropic universe filled with a perfect fluid. If a {\displaystyle a} is the scale factor then ρ ∝ a − 3 ( 1 + w ) . {\displaystyle \rho \propto a^{-3(1+w)}.}
The model uses the Friedmann–Lemaître–Robertson–Walker metric, the Friedmann equations, and the cosmological equations of state to describe the observable universe from approximately 0.1 s to the present. [1]: 605
The comoving distance from an observer to a distant object (e.g. galaxy) can be computed by the following formula (derived using the Friedmann–Lemaître–Robertson–Walker metric): = ′ (′) where a(t′) is the scale factor, t e is the time of emission of the photons detected by the observer, t is the present time, and c is the speed of ...
However, recent findings (the Axis of Evil for example) have suggested that violations of the cosmological principle exist in the universe and thus have called the ΛCDM model into question, with some authors suggesting that the cosmological principle is now obsolete and the Friedmann–Lemaître–Robertson–Walker metric breaks down in the ...
[10] With this term gone from the equation, others derived the Friedmann-Lemaître–Robertson–Walker (FLRW) solution to describe such an expanding universe — a solution built on the assumption of a flat, isotropic, homogeneous universe. The FLRW model became the foundation of the standard model of a universe created by the Big Bang, and ...