The shape of the universe - both flat and torus?
  • CosmicTodd
    So the evidence from WMAP, the Wilkison Anisotropy Probe, seems to have settled the geometry of the universe in the age old question: is it open (saddle-shaped), closed (spherical), or most unlikely of all - flat. Turns out that it's flat based on the size of CBR "cells" observed by WMAP, which match the predicted size for CBR cells in a flat universe. However, it is ALSO posited that the universe is torus shaped (all of these shapes imply that our three dimensional universe is warped in a 4th spatial dimension that we cannot perceive, and the lines that we perceive as straight actually curve in the other dimension.) Anyway, my question (finally) is - how can the universe be both flat and torus shaped? Dr. Gay and Fraser Cain state this pretty clearly in "What Shape is the Universe" episode of AstronomyCast, but don't address the apparent contradiction. Is it just that the term "flat" when used by cosmologist merely means that the parameter Omega = 1 and that parallel lines never diverge or converge (which is true for a torus topology), and not necessarily literally "flat"?
  • John_BradyJohn_Brady
    Hi CosmicTodd,

    Yes the universe could be both flat AND in the shape of a doughnut, torus shape.

    As you say it all depends on the idea of 2 beams of light travelling across space. In a flat universe those beams of light would always stay exactly parallel to each other, and never diverge (closed universe), or converge (open universe).

    Those 2 beams of light could always stay parallel to each other even on a torus, wrapping around going over and under the doughnut shape, or along any surface of the top or bottom.

    So yes, what I get from that is flat doesn't actually mean like a flat sheet, but flat as in the way light travels.

    Thanks for the great question.
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