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A "closed universe" is necessarily a closed manifold. An "open universe" can be either a closed or open manifold. For example, in the Friedmann–Lemaître–Robertson–Walker (FLRW) model, the universe is considered to be without boundaries, in which case "compact universe" could describe a universe that is a closed manifold.
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]
The ratio of the actual density to this critical value is called Ω, and its difference from 1 determines the geometry of the universe: Ω > 1 corresponds to a greater than critical density, >, and hence a closed universe. Ω < 1 gives a low density open universe, and Ω equal to exactly 1 gives a flat universe.
k = +1, 0 or −1 depending on whether the shape of the universe is a closed 3-sphere, flat (Euclidean space) or an open 3-hyperboloid, respectively. [4] If k = +1, then a is the radius of curvature of the universe. If k = 0, then a may be fixed to any arbitrary positive number at one particular time.
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 [10] 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 ...
These are called, respectively, the flat, open and closed universes. [83] Observations, including the Cosmic Background Explorer (COBE), Wilkinson Microwave Anisotropy Probe (WMAP), and Planck maps of the CMB, suggest that the universe is infinite in extent with a finite age, as described by the Friedmann–Lemaître–Robertson–Walker (FLRW ...
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It is the only closed flat 3-manifold with first Betti number zero. Its holonomy group is Z 2 2 {\displaystyle \mathbb {Z} _{2}^{2}} . [ 3 ] It has been suggested as a possible shape of the universe because its complicated geometry can obscure the features in the cosmic microwave background that would arise if the universe is a closed flat ...