What can the detection of a single pair of circles-in-the-sky tell us about the geometry and topology of the Universe?
What can the detection of a single pair of circles-in-the-sky tell us about the geometry and topology of the Universe?
复制标题
检测一对天空中的圆圈可以告诉我们什么关于宇宙的几何形状和拓扑结构的信息？
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
R. Tavakol
中科院分区：
文献类型：
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作者：
B. Mota;M. Rebouças;R. Tavakol
在具有可检测的非平凡空间拓扑的宇宙中，最后一个散射表面包含成对的具有相同温度波动分布的匹配圆——即所谓的天空中的圆。迄今为止，在宇宙微波背景图中对此类圆的近对映对进行的搜索尚未成功。之前我们已经表明，这种搜索的负面结果，如果得到证实，原则上应该足以排除大多数观察者在非常接近平坦（$0<midOmega_{ ext{tot}}-1mid lesssim10^{-5}$）（弯曲）宇宙中可检测到的非平凡空间拓扑。然而，最近我们发现，如果宇宙是平坦的，那么这一图景就会发生根本性的改变。在这种情况下，有许多潜在的圆对与对映性存在较大偏差，尚未被现有搜索探测到。在这里，我们研究在什么条件下检测一对天空中的圆圈可以用来唯一地指定宇宙空间部分的拓扑和几何形状。我们表明，通过检测一对 emph{single} 匹配圆，我们可以推断出空间几何形状是否平坦，如果是，我们将展示如何使用此信息确定宇宙的拓扑（除了一种情况）。我们的结果的一个重要的附加结果是，在搜索匹配的圆对时需要跨越的空中圆参数空间的维数从六个自由度减少到五个自由度，从而显着减少了必要的计算时间。
In a Universe with a detectable nontrivial spatial topology the last scattering surface contains pairs of matching circles with the same distribution of temperature fluctuations --- the so-called circles-in-the-sky. Searches undertaken for nearly antipodal pairs of such circles in cosmic microwave background maps have so far been unsuccessful. Previously we had shown that the negative outcome of such searches, if confirmed, should in principle be sufficient to exclude a detectable non-trivial spatial topology for most observers in very nearly flat ($0<midOmega_{ ext{tot}}-1mid lesssim10^{-5}$) (curved) universes. More recently, however, we have shown that this picture is fundamentally changed if the universe turns out to be {it exactly} flat. In this case there are many potential pairs of circles with large deviations from antipodicity that have not yet been probed by existing searches. Here we study under what conditions the detection of a single pair of circles-in-the-sky can be used to uniquely specify the topology and the geometry of the spatial section of the Universe. We show that from the detection of a emph{single} pair of matching circles one can infer whether the spatial geometry is flat or not, and if so we show how to determine the topology (apart from one case) of the Universe using this information. An important additional outcome of our results is that the dimensionality of the circles-in-the-sky parameter space that needs to be spanned in searches for matching pair of circles is reduced from six to five degrees of freedom, with a significant reduction in the necessary computational time.