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In a universe with zero curvature, the local geometry is flat. The most familiar such global structure is that of Euclidean space, which is infinite in extent. Flat universes that are finite in extent include the torus and Klein bottle. Moreover, in three dimensions, there are 10 finite closed flat 3-manifolds, of which 6 are orientable and 4 ...
The ΛCDM model assumes that the shape of the universe is of zero curvature (is flat) and has an undetermined topology. In 2019, interpretation of Planck data suggested that the curvature of the universe might be positive (often called "closed"), which would contradict the ΛCDM model.
The Friedmann–Lemaître–Robertson–Walker metric is a curved metric which forms the current foundation for the description of the expansion of the universe and the shape of the universe. [citation needed] The fact that photons have no mass yet are distorted by gravity, means that the explanation would have to be something besides photonic ...
Possible shapes of the universe. In terms of the curvature of space-time and the shape of the universe, it can theoretically be closed (positive curvature, or space-time folding in itself as though on a four-dimensional sphere's surface), open (negative curvature, with space-time folding outward), or flat (zero curvature, like the surface of a ...
If k = −1, then (loosely speaking) one can say that i · a is the radius of curvature of the universe. a is the scale factor which is taken to be 1 at the present time. k is the current spatial curvature (when a = 1). If the shape of the universe is hyperspherical and R t is the radius of curvature (R 0 at the present), then a = R t / R 0
The Milne universe is a special case of a more general Friedmann–Lemaître–Robertson–Walker model (FLRW). The Milne solution can be obtained from the more generic FLRW model by demanding that the energy density, pressure and cosmological constant all equal zero and the spatial curvature is negative.
Trying to find a complete and precise definition of singularities in the theory of general relativity, the current best theory of gravity, remains a difficult problem. [1] [2] A singularity in general relativity can be defined by the scalar invariant curvature becoming infinite [3] or, better, by a geodesic being incomplete. [4]
The demand for consistency between a quantum description of matter and a geometric description of spacetime, [189] as well as the appearance of singularities (where curvature length scales become microscopic), indicate the need for a full theory of quantum gravity: for an adequate description of the interior of black holes, and of the very ...