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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.
The lower light cone is characteristic of light cones in flat space—all spacetime coordinates included in the light cone have later times. The upper light cone not only includes other spatial locations at the same time, but also does not include x = 0 {\displaystyle x=0} at future times, and includes earlier times.
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 ...
Timeline from Big Bang to the near cosmological future – Visual representation of the universe's past, present, and future Tiny Graphical timeline from Big Bang to Heat Death – Future scenario if the expansion of the universe will continue forever or not - Timeline uses the log scale for comparison with the double-logarithmic scale in this ...
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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.