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

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 Ω₀ ≈ 1.013 > 1, and the model also predicts temperature correlations in matching circles on the sky⁷.