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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. [3] 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.
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 ...
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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Infinite expansion does not constrain the overall spatial curvature of the universe. It can be open (with negative spatial curvature), flat, or closed (positive spatial curvature), although if it is closed, sufficient dark energy must be present to counteract the gravitational forces or else the universe will end in a Big Crunch. [9]