Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background
J.-P. Luminet, J. Weeks, A. Riazuelo, R. Lehoucq, J.-P. Uzan
Abstract
Cosmology's standard model 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 (Bennett {\it et al.}, 2003 ; Spergel {\it et al.}, 2003). Temperature correlations across the microwave sky match expectations on scales narrower than
60
∘
, yet vanish on scales wider than
60
∘
. Researchers are now seeking an explanation of the missing wide-angle correlations (Contaldi {\it et al.}, 2003 ; Cline {\it et al.}, 2003). One natural approach questions the underlying geometry of space, namely its curvature (Efstathiou, 2003) and its topology (Tegmark {\it et al.}, 2003). 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 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, positively curved space -- the Poincaré dodecahedral space -- which accounts for WMAP's observations with no fine-tuning required. Circle searching (Cornish, Spergel and Starkman, 1998) may confirm the model's topological predictions, while upcoming Planck Surveyor data may confirm its predicted density of
Ω
0
≃1.013>1
. If confirmed, the model will answer the ancient question of whether space is finite or infinite, while retaining the standard Friedmann-Lema\^ıtre foundation for local physics.