A multiconnected topology translates into the fact that any object in space may possess several copies of itself in the observable Universe. For an extended object like the region of emission of the CMB radiation we observe (the so-called last scattering surface) it can happen that it intersects with itself along pairs of circles . In this case;; this is equivalent to say that an observer (located at the center of the last scattering surface) will see the same region of the Universe from different directions. As a consequence;; the temperature fluctuations will match along the intersection of the last scattering surface with itself;; as illustrated in the above figure. This CMP map is simulated for a multi-connected flat space - namely a cubic hypertorus whose length is 3.17 times smaller than the diameter of the last scattering surface.
Cosmologists hope to "hear the shape of space", namely its topology, by analyzing in detail the temperature fluctuations in the cosmic microwave background radiation (CMB). An international team of cosmologists, including researchers from l’Observatoire de Paris, has recently developped a model for the vibrations of the universe. For the first time , they have simulated high resolution CMB maps containing the signatures of a wide class of topologies, for comparison with the forthcoming MAP satellite data in early 2003.
The shape of space
In recent years, cosmologists have become interested in the global shape of space . Previously, most of them had neglected the fact that, even if space is flat on a large scale, it can take many different shapes, for instance that of a doughnut-like hypertorus. A space of a given curvature admits a number a topologies. Indeed, 18 flat topologies along with an infinite number of spherical and hyperbolic ones are theoretical candidates to describe the shape of physical space.
Jean-Pierre Luminet | alfa
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