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Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background


The current ‘standard model’ of cosmology posits an infinite flat universe forever expanding under the pressure of dark energy. First-year data from the Wilkinson Microwave Anisotropy Probe (WMAP) confirm this model to spectacular precision on all but the largest scales1,2. Temperature correlations across the microwave sky match expectations on angular scales narrower than 60° but, contrary to predictions, vanish on scales wider than 60°. Several explanations have been proposed3,4. One natural approach questions the underlying geometry of space—namely, its curvature5 and topology6. In an infinite flat space, waves from the Big Bang would fill the universe on all length scales. The observed lack of temperature correlations on scales beyond 60° means that the broadest waves are missing, perhaps because space itself is not big enough to support them. Here we present a simple geometrical model of a finite space—the Poincaré dodecahedral space—which accounts for WMAP's observations with no fine-tuning required. The predicted density is Ω0 ≈ 1.013 > 1, and the model also predicts temperature correlations in matching circles on the sky7.

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Figure 1: Comparison of the WMAP power spectrum to that of Poincaré dodecahedral space and an infinite flat universe.
Figure 2: Wavelengths of density fluctuations are limited by the size of a finite ‘wraparound’ universe.
Figure 3: Spherical pentagons and dodecahedra fit snugly, unlike their euclidean counterparts.
Figure 4: Values of the mass-energy density parameter Ω0 for which the Poincaré dodecahedral space agrees with WMAP's results.


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J.R.W. thanks the MacArthur Foundation for support.

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Correspondence to Jeffrey R. Weeks.

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Luminet, JP., Weeks, J., Riazuelo, A. et al. Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background. Nature 425, 593–595 (2003).

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