In the standard model of cosmology, space has been flat and infinite ever since the universe underwent a short period of extremely rapid expansion called inflation shortly after the Big Bang. Moreover, we now know that the expansion of the universe is actually accelerating due to a mysterious repulsive force caused by “dark” energy (see “Dark energy” Physics World May 2004 pp37-42).
Cosmologists usually assume that the universe is simply connected like a plane, which means there is only one direct path for light to travel from a source to an observer. A simply connected Euclidean or hyperbolic universe would indeed be infinite, but if the universe is multiply connected, like a torus, there would be many different possible paths. This means that an observer would see multiple images of each galaxy and could easily misinterpret them as distinct galaxies in an endless space, much as a visitor to a mirrored room has the illusion of seeing a crowd. Could we, in fact, be living in such a cosmic hall of mirrors?
The article goes into extensive detail the anomalies in cosmic microwave background radiation that suggest we are not in a simply-connected space. Fluctuations in the temperature of that background radiation can be expressed as combinations of the vibrational modes of space itself. However, vibrational modes corresponding to very long wavelengths (ie, large scales) are very weakly represented, implying that space simply isn’t as big as we thought it was. However, by adopting a different geometrical model, the anomalies can be explained:
…[T]he best candidate to fit the observed power spectrum is a well-proportioned space called the PoincarÃ© dodecahedral space.
This space may be represented by a polyhedron with 12 pentagonal faces, with opposite faces being “glued” together after a twist of 36Â° (figure 3). This is the only consistent way to obtain a spherical (i.e. positively curved) space from a dodecahedron: if the twist was 108Â°, for example, we would end up with a radically different hyperbolic space. The PoincarÃ© dodecahedral space is essentially a multiply connected variant of a simply connected hypersphere, although its volume is 120 times smaller.
A rocket leaving the dodecahedron through a given face immediately re-enters through the opposite face, and light propagates such that any observer whose line-of-sight intercepts one face has the illusion of seeing a slightly rotated copy of their own dodecahedron. This means that some photons from the cosmic microwave background, for example, would appear twice in the sky.
What is fascinating about this is that the size of the dodecahedral universe can be estimated, using data from astronomical observations about the expansion rate of the universe and mass-energy densities in space. The authors found that the PoincarÃ© dodecahedron space is 43 billion light-years wide, compared to 53 billion light-years for the standard model. That’s a 20% smaller universe – and also implies that we should be able to see repetition in the sky across very large scales. The rest of the article goes on to discuss the search for such repetitions.
Is the universe a dodacahedron? We still are not sure, but it is certainly possible, and even plausible. Which opens up a whole new door for science fiction…
UPDATE: Shamus models the universe.