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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 ...
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 ...
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 ...
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.
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 ...
[1] [2] [3] Nonetheless, some physicists have proposed that a "Big Crunch-style" event could result from a dark energy fluctuation. [4] The hypothesis dates back to 1922, with Russian physicist Alexander Friedmann creating a set of equations showing that the end of the universe depends on its density. It could either expand or contract rather ...
The local geometry of the universe is determined by whether the relative density Ω is less than, equal to or greater than 1. From top to bottom: a spherical universe with greater than critical density (Ω>1, k>0); a hyperbolic, underdense universe (Ω<1, k<0); and a flat universe with exactly the critical density (Ω=1, k=0). The spacetime of ...