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The three-torus model of the universe, or informally doughnut theory of the universe, is a proposed model describing the shape of the universe as a three-dimensional torus. The name comes from the shape of a doughnut, whose surface has the topology of a two-dimensional torus.
Alexi Starobinski and Yakov B. Zeldovich proposed the model in 1984 from the Landau Institute in Moscow; however, the basis for his theory began much earlier than 1984. The foundation for any knowledge of the shape of the universe began in the mid-1960s with the discovery of cosmic microwave background (CMB) by Bell Labs. Greater understanding of the universe's CMB provided greater understanding of the universe's topology; therefore, in a quest for cosmic understanding, NASA supported two explorer satellites, the Cosmic Background Explorer (COBE) in 1989 and the Wilkinson Microwave Anisotropy Probe (WMAP) in 2001, which have gathered more information on CMB.
The Cosmic Background Explorer was an explorer satellite launched in 1989 by NASA that used a Far Infrared Absolute Spectrometer (FIRAS) to measure the radiation of the universe. Led by researchers John C. Mather and George Smoot, COBE was able to obtain precise readings of radiation frequencies across the universe. With data on the universe’s radiation distribution, Mather and Smoot discovered small discrepancies in temperature fluctuation known as anisotropies throughout the universe. The finding of anisotropies led Mather and Smoot to conclude the universe consists of regions of varying densities. In the early stages of the universe, these denser regions of the cosmos were responsible for attracting the matter that ultimately became galaxies and solar systems. In “Microwave Background Anisotropy in a Toroidal Universe” by Daniel Stevens, Douglas Scott, and Joseph Silk of University of California Berkeley, the cosmologists proposed the isotropic universe suggests a complicated geometric structure. The researchers argued the density fluctuations reported by COBE proved “multiply connected universes are possible, [and] the simplest [and most probable multiply connected universe] is the three-dimensional torus.” Additionally, the journal concludes a torus shaped universe is compatible with COBE data if the diameter of the torus' tube is at least 80% greater than the torus’ horizontal diameter. Thus, COBE provided researchers with the first concrete evidence for a torus-shaped universe. COBE was eventually decommissioned by NASA on December 23, 1993.
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