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

Naturevolume 425pages593595 (2003) | Download Citation



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

Author information


  1. Observatoire de Paris, 92195, Meudon Cedex, France

    • Jean-Pierre Luminet
    •  & Roland Lehoucq
  2. 15 Farmer Street, Canton, New York, 13617-1120, USA

    • Jeffrey R. Weeks
  3. CEA/Saclay, 91191, Gif-sur-Yvette Cedex, France

    • Alain Riazuelo
    •  & Roland Lehoucq
  4. Laboratoire de Physique Théorique, Université Paris XI, 91405, Orsay Cedex, France

    • Jean-Philippe Uzan


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Competing interests

The authors declare that they have no competing financial interests.

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Correspondence to Jeffrey R. Weeks.

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