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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 density parameter is the average density of the universe divided by the critical energy density, that is, the mass energy needed for a universe to be flat. Put another way, If Ω = 1, the universe is flat. If Ω > 1, there is positive curvature. If Ω < 1, there is negative curvature.
Such a space is called a "flat space" or Euclidean space. [citation needed] Whether the universe is “flat″ could determine its ultimate fate; whether it will expand forever, or ultimately collapse back into itself. The geometry of spacetime has been measured by the Wilkinson Microwave Anisotropy Probe (WMAP) to be nearly flat
The zero-energy universe hypothesis proposes that the total amount of energy in the universe is exactly ... Imagine a man wants to build a hill on a flat piece of ...
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 [7] 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 ...
A flat universe implies a balance between gravitational potential energy and other energy forms, requiring no additional energy to be created. [ 141 ] [ 142 ] The Big Bang theory is built upon the equations of classical general relativity, which are not expected to be valid at the origin of cosmic time, as the temperature of the universe ...
If k is positive, then the universe is "closed": starting off on some paths through the universe return to the starting point. Such a universe is analogous to a sphere: finite but unbounded. If k is negative, then the universe is "open": infinite and no paths return. If k = 0, then the universe is Euclidean (flat) and infinite. [4]: 69
A de Sitter universe is a cosmological solution to the Einstein field equations of general relativity, named after Willem de Sitter.It models the universe as spatially flat and neglects ordinary matter, so the dynamics of the universe are dominated by the cosmological constant, thought to correspond to dark energy in our universe or the inflaton field in the early universe.