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The density parameter Ω is defined as the ratio of the actual (or observed) density ρ to the critical density ρ c of the Friedmann universe. The relation between the actual density and the critical density determines the overall geometry of the universe; when they are equal, the geometry of the universe is flat (Euclidean).
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 ...
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 fraction of the total energy density of our (flat or almost flat) universe that is dark energy, , is estimated to be 0.669 ± 0.038 based on the 2018 Dark Energy Survey results using Type Ia supernovae [8] or 0.6847 ± 0.0073 based on the 2018 release of Planck satellite data, or more than 68.3 % (2018 estimate) of the mass–energy density ...
e. 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: where is the scale factor of the universe and the dots indicate derivatives by proper time. The expansion of the universe is said to be ...
Flatness problem. 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 ...
For k > 1, the density function tends to zero as x approaches zero from above, increases until its mode and decreases after it. The density function has infinite negative slope at x = 0 if 0 < k < 1, infinite positive slope at x = 0 if 1 < k < 2 and null slope at x = 0 if k > 2. For k = 1 the density has a finite negative slope at x = 0.
The fluid has a constant density by definition. It is given by = =, where = / is the Einstein gravitational constant. [3] [5] It may be counterintuitive that the density is the mass divided by the volume of a sphere with radius , which seems to disregard that this is less than the proper radius, and that space inside the body is curved so that the volume formula for a "flat" sphere shouldn't ...