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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.
An important parameter in fate of the universe theory is the density parameter, omega (), defined as the average matter density of the universe divided by a critical value of that density. This selects one of three possible geometries depending on whether Ω {\displaystyle \Omega } is equal to, less than, or greater than 1 {\displaystyle 1} .
The theory of general relativity also described the universe as restless. Einstein realized that for a static universe to exist—which was observed at the time—an anti-gravity would be needed to counter the gravity contracting the universe together, adding an extra force that would ruin the equations in the theory of relativity.
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.
In 1994, development of the theory resumed [11] following the publication of a work by Nathan Rosen, [12] in which Rosen described a special case of closed universe.
Einstein's static universe is closed (i.e. has hyperspherical topology and positive spatial curvature), and contains uniform dust and a positive cosmological constant with value precisely = /, where is Newtonian gravitational constant, is the energy density of the matter in the universe and is the speed of light.
A closed timelike curve can be created if a series of such light cones are set up so as to loop back on themselves, so it would be possible for an object to move around this loop and return to the same place and time that it started.
Many attempts to generate scenarios for closed timelike curves have been suggested, and the theory of general relativity does allow them in certain circumstances. Some theoretical solutions in general relativity that contain closed timelike curves would require an infinite universe with certain features that our universe does not appear to have, such as the universal rotation of the Gödel ...