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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.
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
In the case of the flatness problem, the parameter which appears fine-tuned is the density of matter and energy in the universe. This value affects the curvature of space-time, with a very specific critical value being required for a flat universe. The current density of the universe is observed to be very close to this critical value.
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 ...
In other words, the energy (relative to the origin) of a co-moving particle in free-fall is conserved. General relativity merely adds a connection between the spatial curvature of the universe and the energy of such a particle: positive total energy implies negative curvature and negative total energy implies positive curvature.
The Einstein–de Sitter universe is a model of the universe proposed by Albert Einstein and Willem de Sitter in 1932. [1] On first learning of Edwin Hubble's discovery of a linear relation between the redshift of the galaxies and their distance, [2] Einstein set the cosmological constant to zero in the Friedmann equations, resulting in a model of the expanding universe known as the Friedmann ...