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

2003/10/01 by J. -P. Luminet, Jean‐Pierre Luminet, Jeffrey R. Weeks +7 · 11 citations
Mathematics · Physics and Astronomy · #Anisotropy #Astrophysics #Big Bang (financial markets) #CMB cold spot #Cosmic background radiation #Cosmic microwave background #Cosmology #Cosmology and Gravitation Theories #Curvature #Dark Matter and Cosmic Phenomena #Dodecahedron #Galaxies: Formation, Evolution, Phenomena #Geometry #Mathematics #Physics #Quantum mechanics #Space (punctuation) #Theoretical physics #Topology (electrical circuits) #Universe #astro-ph #gr-qc

paper · pdf · doi:10.1038/nature01944

published as Nature 425 (2003) 593 · 10 pages, 4 figures. This is a slightly longer version of the paper published in Nature 425, p. 593, 2003

openalex publication_date 2003/10/01 · arxiv created 2003/10/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 Ω₀ ≃ 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.

Citations

• Can we have inflation with > 1?*
• Suppressing the lower multipoles in the CMB anisotropies
• Topological lensing in spherical spaces
• First‐Year Wilkinson Microwave Anisotropy Probe ( WMAP ) Observations: Preliminary Maps and Basic Results
• High resolution foreground cleaned CMB map from WMAP
• First‐Year Wilkinson Microwave Anisotropy Probe ( WMAP ) Observations: Determination of Cosmological Parameters

Cited by

• A test of the Poincaré dodecahedral space topology hypothesis with the WMAP CMB data
• Holographic explanation of wide-angle power correlation suppression in the cosmic microwave background radiation
• Effect of the length of inflation on angular TT and TE power spectra in power-law inflation
• Interacting generalized ghost dark energy in a non-flat universe
• Disformal inflation
• The study of topology of the Universe using multipole vectors
• Platonic polyhedra tune the 3-sphere: harmonic analysis on simplices
• WHICH FLRW COMOVING 3-MANIFOLD IS PREFERRED OBSERVATIONALLY AND THEORETICALLY?
• The residual gravity acceleration effect in the Poincaré dodecahedral space
• CMB anisotropy of spherical spaces
• 3-manifold [wikipedia]