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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 overall geometry of the universe is determined by whether the Omega cosmological parameter is less than, equal to or greater than 1. Shown from top to bottom are a closed universe with positive curvature, a hyperbolic universe with negative curvature and a flat universe with zero curvature.
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.
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
Because the universe is expanding, is smaller in the past and larger in the future. Extrapolating back in time with certain cosmological models will yield a moment when the scale factor was zero; our current understanding of cosmology sets this time at 13.787 ± 0.020 billion years ago. If the universe continues to expand forever, the scale ...
The chronology of the universe describes the history and future of the universe according to Big Bang cosmology.. Research published in 2015 estimates the earliest stages of the universe's existence as taking place 13.8 billion years ago, with an uncertainty of around 21 million years at the 68% confidence level.
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.