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The term Friedmann equation sometimes is used only for the first equation. [3] In these equations, R(t) is the cosmological scale factor , G N {\displaystyle G_{N}} is the Newtonian constant of gravitation , Λ is the cosmological constant with dimension length −2 , ρ is the energy density and p is the isotropic pressure.
In an expanding universe, fluids with larger equations of state disappear more quickly than those with smaller equations of state. This is the origin of the flatness and monopole problems of the Big Bang : curvature has w = − 1 / 3 {\displaystyle w=-1/3} and monopoles have w = 0 {\displaystyle w=0} , so if they were around at the time of the ...
Alternatively, as before, k may be taken to belong to the set {−1 ,0, +1} (for negative, zero, and positive curvature respectively). Then r is unitless and a(t) has units of length. When k = ±1, a(t) is the radius of curvature of the space, and may also be written R(t). Note that when k = +1, r is essentially a third angle along with θ and φ.
In 1922, Alexander Friedmann derived his Friedmann equations from Einstein field equations, showing that the universe might expand at a rate calculable by the equations. [24] The parameter used by Friedmann is known today as the scale factor and can be considered as a scale invariant form of the proportionality constant of Hubble's law. Georges ...
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 ...
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. Later, with cooling from the ...
The deceleration parameter in cosmology is a dimensionless measure of the cosmic acceleration of the expansion of space in a Friedmann–Lemaître–Robertson–Walker universe. It is defined by: q = d e f − a ¨ a a ˙ 2 {\displaystyle q\ {\stackrel {\mathrm {def} }{=}}\ -{\frac {{\ddot {a}}a}{{\dot {a}}^{2}}}} where a {\displaystyle a} is ...
In modern physical cosmology, the cosmological principle is the notion that the spatial distribution of matter in the universe is uniformly isotropic and homogeneous when viewed on a large enough scale, since the forces are expected to act equally throughout the universe on a large scale, and should, therefore, produce no observable inequalities in the large-scale structuring over the course ...