Revenge of Ω

Maybe the Universe is just a giant dodecahedron?

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 Poincaré dodecahedral space.

This space may be represented by a polyhedron with 12 pentagonal faces, with opposite faces being “glued” together after a twist of 36° (figure 3). This is the only consistent way to obtain a spherical (i.e. positively curved) space from a dodecahedron: if the twist was 108°, for example, we would end up with a radically different hyperbolic space. The Poincaré 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 Poincaré 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.

2 thoughts on “Revenge of Ω”

  1. “…and also implies that we should be able to see repetition in the sky across very large scales.”

    Except that even if we did, we might not recognize it, since the different images of the same places we would see would be from different angles, and would be different ages due to being different path lengths away from us.

    Some of those quasars we see out there might well be our own galaxy. But how would we know?

    A different point: if the universe is about 13.5 billion years old (the current estimate) and the round-trip distance is 43 billion light years, then there hasn’t been enough time for light to propagate all the way around, full circle.

    And even if it had, it would be so attenuated that we probably couldn’t detect it.

  2. oops! My apologies for forgetting to link to the actual article – it’s here on PhysicsWeb.

    Steven, the math behind the prediction for repetition in the sky is pretty well-established, according to the article:

    If physical space is indeed smaller than the observable universe, some points on the map of the cosmic microwave background will have several copies. As first shown by Neil Cornish of Montana State University and co-workers in 1998, these ghost images would appear as pairs of so-called matched circles in the cosmic microwave background where the temperature fluctuations should be the same (figure 4). This “lensing” effect, which can be precisely calculated, is thus purely attributable to the topology of the universe.

    Due to its 12-sided regular shape, the Poincaré dodecahedral model actually predicts six pairs of diametrically opposite matched circles with an angular radius of 10-50°, depending on the precise values of cosmological parameters such as the mass-energy density.

    Note that they are talking about points on the cosmic microwave background, not the optical spectrum. The CMB is diffuse and very old, and its not linear distance but rather the angular span across the sky that would matter. Optically speaking, Olber’s Paradox pretty much rules out seeing repetition anyway.

    With respect to the age/distance issue, it is true that the universe is only 13.7 byo at best estimate. However the horizon radius is much larger – for a flat universe according to the standard model, the horizon radius is actually 57 billion light-years. Remember that the physical distance that light has to travel is larger because of the expansion of teh universe, assumedly isotropically. The 43 bly size estimate given by the Poincare dodecahedron model should be properly compared to the 53 bly size of the horizon radius of the observable universe, not just the linear age in elapsed time.

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