its global geometry, which concerns the topology of the universe as a whole.its local geometry, which predominantly concerns the curvature of the universe, particularly the observable universe, and.Shape of the observable universe Īs stated in the introduction, there are two aspects to consider: At present, the only possibility to elucidate such global properties relies on observational data, especially the fluctuations (anisotropies) of the temperature gradient field of the Cosmic Microwave Background (CMB). Thus, Einstein's field equations determine only the local geometry but have absolutely no say on the topology of the universe. Therefore, only the local geometric properties of the universe become theoretically accessible. Physical cosmology is based on the theory of General Relativity, a physical picture cast in terms of differential equations. Arguments have been put forward that the observational data best fit with the conclusion that the shape of the global universe is infinite and flat, but the data is also consistent with other possible shapes, such as the so-called Poincaré dodecahedral space, the multiply connected three-torus, and the Sokolov–Starobinskii space ( quotient of the upper half-space model of hyperbolic space by a 2-dimensional lattice). The family of models that most theorists use is the Friedmann–Lemaître–Robertson–Walker (FLRW) models. In formal terms, this is a 3-manifold model corresponding to the spatial section (in comoving coordinates) of the four-dimensional spacetime of the universe. Theorists have been trying to construct a formal mathematical model of the shape of the (entire) universe relating connectivity, curvature and boundedness. On the other hand, any non-zero curvature is possible for a sufficiently large curved universe (analogous to how a small portion of a sphere can look flat). The issue of simple versus multiple connectivity is even more uncertain and as of 2023 has not yet been decided based on astronomical observation. In this regard, experimental data from various independent sources ( WMAP, BOOMERanG, and Planck for example) interpreted within the standard family of metrics imply that the universe is flat to within only a 0.4% margin of error of the curvature density parameter. The shape of the universe remains a matter of debate in physical cosmology. Yet, in the case of simply connected spaces, flatness implies infinitude. For example, a multiply connected space may be flat and finite, as illustrated by the three-torus. Although it is usually assumed in the literature that a flat or negatively curved universe is infinite, this need not be the case if the topology is not the trivial one. For example, a universe with positive curvature is necessarily finite. There are certain logical connections among these properties.
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