宇宙微波背景谱及分形空间分辨率的确定
The Cosmic Microwave Background Spectrum and a Determination of Fractal Space Dimensionality
摘要：
简要评述了从天体物理学和其他领域限制分形空间维数的可能性。假设这种维数为$3 + ε$，则可从COBE卫星数据推断出对$ε$的限制。利用推广到非整数空间维的普朗克辐射分布拟合了现有的宇宙微波背景辐射谱数据。我们的分析表明，CMBR谱的形状，它不依赖于绝对归一化，正确地描述了从这个分布提供的绝对温度等于2.726 $\pm$ $0.003\times 10^{-2}$ K和$ε= - (0.957 \pm 0.006) \times 10^{-5}$。这个值为$ε$示出是一致的，发现在一个非常不同的空间尺度上的基础上的量子场现象。$|ε|$被解释为空间维度可能偏离3的上限。换句话说，这是与脱钩时代相比，空间维度在空间和时间尺度上应该经历的最大波动。
英文摘要：
The possibility to constrain fractal space dimensionality from Astrophysics and other areas is briefly reviewed. Assuming such dimensionality to be $3 + ε$, a limit to $ε$ can be inferred from COBE satellite data. The available data for the cosmic microwave background radiation spectrum are fitted by a Planck's radiation distribution generalized to non integer space dimensionality. Our analysis shows that the shape of the CMBR spectrum, which does not depend on the absolute normalization, is correctly described from this distribution provided the absolute temperature is equal to 2.726 $\pm$ $0.003\times 10^{-2}$ K and $ε= - (0.957 \pm 0.006) \times 10^{-5}$. This value for $ε$ is shown to be consistent with what is found on a very different spatial scale based on a quantum field phenomenon. The $|ε|$ is interpreted as an upper limit for how much space dimensionality could have deviated from three. In other words, this is the maximum fluctuation space dimensionality should have experienced in a spatial and temporal scale compared to that of the decoupling era.
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