Cosmic Topology: Studying The Shape And Size Of Our Universe

Mathematics – Logic

Scientific paper

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Scientific paper

The question of the size and the shape of our universe is a very old problem that has received considerable attention over the past few years. The simplest cosmological model predicts that the mean density of the universe is very close to the critical density, admitting a local geometry of the universe that is flat. Current results from different cosmological observations confirm this to the percent level accuracy. General Relativity (being a local theory) only determines local geometry, which allows for the possibility of a multiply connected universe with a zero (or small) curvature. To study the global shape, or topology, of the universe, one can use cosmological observations on large scales. In this project we investigate the possibility of a ``small universe'', that is, a compact finite space, by searching for planar symmetries in the CMB anisotropy maps provided by the five-year WMAP observations in two foreground cleaned maps (WMAP ILC map and the Tegmark, et al. (TOH) map ). Our results strongly suggest that the small universe model is not a viable topology for the universe.

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