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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 spacetime of ...
For a flat (zero curvature) or a hyperbolic (negative curvature) spatial geometry, the topology can be either compact or infinite. [8] Many textbooks erroneously state that a flat or hyperbolic universe implies an infinite universe; however, the correct statement is that a flat universe that is also simply connected implies an infinite universe ...
This term originally was used as a means to determine the spatial geometry of the universe, where ρ c is the critical density for which the spatial geometry is flat (or Euclidean). Assuming a zero vacuum energy density, if Ω is larger than unity, the space sections of the universe are closed; the universe will eventually stop expanding, then ...
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 ...
The geometry of spacetime has been measured by the Wilkinson Microwave Anisotropy Probe (WMAP) to be nearly flat. According to the WMAP 5-year results and analysis, “WMAP determined that the universe is flat, from which it follows that the mean energy density in the universe is equal to the critical density (within a 1%
Recent observations conclude, from 7.5 billion years after the Big Bang, that the expansion rate of the universe has probably been increasing, commensurate with the Open Universe theory. [9] However, measurements made by the Wilkinson Microwave Anisotropy Probe suggest that the universe is either flat or very close to flat. [2]
Some physicists, such as Lawrence Krauss, Stephen Hawking or Alexander Vilenkin, call or called this state "a universe from nothingness", although the zero-energy universe model requires both a matter field with positive energy and a gravitational field with negative energy to exist. [2]
The cosmological constant was originally introduced in Einstein's 1917 paper entitled “The cosmological considerations in the General Theory of Reality”. [2] Einstein included the cosmological constant as a term in his field equations for general relativity because he was dissatisfied that otherwise his equations did not allow for a static universe: gravity would cause a universe that was ...