Well‐proportioned universes suppress the cosmic microwave background quadrupole
Well‐proportioned universes suppress the cosmic microwave background quadrupole
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匀称的宇宙抑制宇宙微波背景四极子
DOI：
10.1111/j.1365-2966.2004.07922.x
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发表时间：
2004
影响因子：
4.8
通讯作者：
R. Lehoucq
中科院分区：
文献类型：
--
作者：
J. Weeks;J. Luminet;A. Riazuelo;R. Lehoucq
一个广泛流传的神话声称，所有的小宇宙模型都抑制了宇宙微波背景（CMB）四极。实际上，根据低阶模相对于高阶模的强弱，有的模型抑制四极子，有的模型提高四极子。初等几何推理表明，模型的最大维数决定了CMB功率谱l（l + 1）C l /2π有效开始的粗略值l min;对于宇宙学相关的模型，l min ≤ 3。更令人惊讶的是，基本的几何推理表明，进一步减少模型的较小尺寸-其最大尺寸保持固定-用于提升相对于光谱的高-l部分的l min附近的模式，而不是像人们天真地期望的那样抑制它们。因此，在最大维度与视界直径相当或小于视界直径的模型中，低阶Cl在均匀空间（在所有方向上维度近似相等的空间）中往往相对较弱，但在奇怪比例空间（在某些方向上明显较长而在其他方向上较短的空间）中相对较强。我们详细说明了这一原则的特殊情况下，矩形3环面和球形空间。我们的结论是，均匀的空间，使最好的候选人的低CMB四极COBE和WMAP观察到的拓扑解释。
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 l min at which the CMB power spectrum l(l + 1) C l /2π effectively begins; for cosmologically relevant models, l min ≤ 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 l min 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 C l 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.