2003/12/31 by Jeffrey R. Weeks, Jeffrey Weeks, Jean‐Pierre Luminet +4 · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #astro-ph
paper · pdf · doi:10.1111/j.1365-2966.2004.07922.x
published as Mon.Not.Roy.Astron.Soc. 352 (2004) 258 · v1: 10 pages, 1 figure. v2: improved exposition of competing mode-suppression and mode-enhancement effects, coincides with published version, 12 pages, 1 figure
openalex publication_date 2004/07/01 · arxiv created 2004/07/05 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A widespread myth asserts that all small universe models suppress the cosmic microwave background (CMB) quadrupole. In actual fact, some models suppress the quadrupole while others elevate it, according to whether their low-order modes are weak or strong relative to their high-order modes. Elementary geometrical reasoning shows that a model's largest dimension determines the rough value ℓmin at which the CMB power spectrum ℓ(ℓ+ 1) Cℓ/2π effectively begins; for cosmologically relevant models, ℓmin≤ 3. More surprisingly, elementary geometrical reasoning shows that further reduction of a model's smaller dimensions – with its largest dimension held fixed – serves to elevate modes in the neighbourhood of ℓmin relative to the high-ℓ portion of the spectrum, rather than suppressing them as one might naively expect. Thus among the models whose largest dimension is comparable to or less than the horizon diameter, the low-order Cℓ tend to be relatively weak in well-proportioned spaces (spaces whose dimensions are approximately equal in all directions) but relatively strong in oddly proportioned spaces (spaces that are significantly longer in some directions and shorter in others). We illustrate this principle in detail for the special cases of rectangular 3-tori and spherical spaces. We conclude that well-proportioned spaces make the best candidates for a topological explanation of the low CMB quadrupole observed by COBE and WMAP.