1. Observatoire de Paris, 92195 Meudon Cedex, France
2. 15 Farmer Street, Canton, New York 13617-1120, USA
3. CEA/Saclay, 91191 Gif-sur-Yvette Cedex, France
4. Laboratoire de Physique Théorique, Université Paris XI, 91405 Orsay Cedex, France

Correspondence to: Jeffrey R. Weeks² Email: weeks@northnet.org

Abstract

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 scales^{1, 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 proposed^{3, 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 ₀ 1.013 > 1, and the model also predicts temperature correlations in matching circles on the sky⁷.

1. Observatoire de Paris, 92195 Meudon Cedex, France
2. 15 Farmer Street, Canton, New York 13617-1120, USA
3. CEA/Saclay, 91191 Gif-sur-Yvette Cedex, France
4. Laboratoire de Physique Théorique, Université Paris XI, 91405 Orsay Cedex, France

Correspondence to: Jeffrey R. Weeks² Email: weeks@northnet.org