Shape of the universe

The shape or geometry of the Universe includes both local geometry in the observable Universe and global geometry, which we may or may not be able to measure. Shape can refer to curvature and topology. More formally, the subject in practice investigates which 3-manifold corresponds to the spatial section in comoving coordinates of the four-dimensional space-time of the Universe. Cosmologists normally work with a given space-like slice of spacetime called the comoving coordinates. In terms of observation, the section of spacetime that can be observed is the backward light cone (points within the cosmic light horizon, given time to reach a given observer). If the observable Universe is smaller than the entire Universe (in some models it is many orders of magnitude smaller), one cannot determine the global structure by observation: one is limited to a small patch.
Among the Friedmann–Lemaître–Robertson–Walker (FLRW) models, the presently most popular shape of the Universe found to fit observational data according to cosmologists is the infinite flat model, while other FLRW models include the Poincaré dodecahedral space and the Picard horn. The data fit by these FLRW models of space especially include the Wilkinson Microwave Anisotropy Probe (WMAP) and Planck maps of cosmic background radiation. NASA released the first WMAP cosmic background radiation data in February 2003, while a higher resolution map regarding Planck data was released by ESA in March 2013. Both probes have found almost perfect agreement with inflationary models and the standard model of cosmology, describing a flat, homogeneous universe dominated by dark matter and dark energy.
                                          

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The shape of the universe is the local and global geometry of the universe, in terms of both curvature and topology (though, strictly speaking, it goes beyond both). When physicists describe the universe as being flat or nearly flat, they're talking geometry: how space and time are warped according to general relativity. When they talk about whether it is open or closed, they're referring to its topology. Although the shape of the universe is still a matter of debate in physical cosmology, based on the recent Wilkinson Microwave Anisotropy Probe (WMAP) measurements "We now know that the universe is flat with only a 0.4% margin of error", according to NASA scientists. Theorists have been trying to construct a formal mathematical model of the shape of the universe. In formal terms, this is a 3-manifold model corresponding to the spatial section (in comoving coordinates) of the 4-dimensional space-time of the universe. The model most theorists currently use is the so-called Friedmann–Lemaître–Robertson–Walker (FLRW) model. According to cosmologists, on this model the observational data best fit with the conclusion that the shape of the universe is infinite and flat, but the data are also consistent with other possible shapes, such as the so-called Poincaré dodecahedral spaceand the Picard horn.