Poincaré space may be represented by a dodecahedron (a regular polyhedron with 12 pentagonal faces) whose opposite faces are glued after a 36° twist ; such a space is positively curved, and is a multiply connected variant of the hypersphere, with a volume 120 times smaller. A rocket going out of the dodecahedron by crossing a given face immediately re-enters by the opposite face. Propagation of light rays is such that any observer whose line-of-sight intercepts one face has the illusion to see inside a copy of his own dodecahedron (since his line-of-sight re-enters the original dodecahedron from the opposite side).
Perhaps the most fundamental challenge is to link the present-day topology of space to a quantum origin, since general relativity does not allow for topological changes during the course of cosmic evolution. A quantum theory of gravity could allow us to address this problem, but there is currently no indication about how such a unified theory might actually describe the emergence of multiply connected spaces.
It is clearly premature to claim a highly significant detection of the topology of the Universe based on just one simple analysis of the first year WMAP ILC cosmic microwave background map.
However, the plots are striking and it seems prudent to release them to the scientific community while a companion paper is prepared with formal statistical analyses.
Whether or not the matched circles found are just coincidence or due to global geometry, it is clear that temperature fluctuations around 12 dodecahedrally spaced circles of radius 11 + 1° in the WMAP ILC map correlate unusually well in their respective pairs when a phase shift of 36°, corresponding to a left-handed screw motion, is applied.
2008-09-29 | achtphasen | 12:28:37 | 
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