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The Friedmann equations, also known as the Friedmann–Lemaître (FL) equations, are a set of equations in physical cosmology that govern cosmic expansion in homogeneous and isotropic models of the universe within the context of general relativity.
Relativisitic cosmology models based on the FLRW metric and obeying the Friedmann equations are called FRW models. [6]: 73 Direct observation of stars has shown their velocities to be dominated by radial recession, validating these assumptions for cosmological models.
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)}.}
This combination greatly simplifies the equations of general relativity into a form called the Friedmann equations. These equations specify the evolution of the scale factor the universe in terms of the pressure and density of a perfect fluid. The evolving density is composed of different kinds of energy and matter, each with its own role in ...
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 ...
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 radiation was the dominant influence on the expansion of the universe.
The classic solution of the Einstein field equations that describes a homogeneous and isotropic universe was called the Friedmann–Lemaître–Robertson–Walker metric, or FLRW, after Friedmann, Georges Lemaître, Howard P. Robertson and Arthur Geoffrey Walker, who worked on the problem in the 1920s and 30s independently of Friedmann.
Cosmic expansion is a key feature of Big Bang cosmology. It can be modeled mathematically with the Friedmann–Lemaître–Robertson–Walker metric (FLRW), where it corresponds to an increase in the scale of the spatial part of the universe's spacetime metric tensor (which governs the size and geometry of spacetime). Within this framework, the ...