标题： 紧凑双曲宇宙中的CMB各向异性II：COBE地图和限制 显示英文标题

标题： CMB Anisotropy in Compact Hyperbolic Universes II: COBE Maps and Limits

摘要： 我们使用论文I中描述的图像正则化方法计算了紧凑双曲宇宙模型中的CMB各向异性，包括“视线”积分的Sachs-Wolfe效应以及最后散射面项。我们通过将理论上的像素-像素温度相关函数与COBE-DMR数据进行对比，计算了一组模型的贝叶斯概率。我们的结果显示，紧凑性受到了强烈的限制：如果宇宙相对于“视界”大小较小时，地图中会出现无法与观测结果相协调的相关性。这一结论在很大程度上不受宇宙物质成分的影响，特别是存在宇宙常数的情况下也是如此。如果宇宙的大小与“视界”相当，那么似然函数将非常依赖于流形相对于天空的取向。虽然大多数取向可能会被强烈排除，但有时对于特定取向，预测的相关模式会比传统无限模型更受欢迎。我们使用的完整贝叶斯分析是对COBE地图所能进行的最全面的统计测试，考虑了理论天空中所有可能的信号及其方差，特别是高度各向异性的相关性。我们表明，用于比较理论预测与数据的标准视觉度量（如各向同性化的功率谱$C_\ell$）在小而紧凑的空间中并不那么有用，因为这与统计各向同性性的破坏有关，从而导致宇宙学方差增强。 显示英文摘要

摘要： We calculate the CMB anisotropy in compact hyperbolic universe models using the regularized method of images described in paper-I, including the 'line-of-sight `integrated Sachs-Wolfe' effect, as well as the last-scattering surface terms. We calculate the Bayesian probabilities for a selection of models by confronting our theoretical pixel-pixel temperature correlation functions with the COBE-DMR data. Our results demonstrate that strong constraints on compactness arise: if the universe is small compared to the `horizon' size, correlations appear in the maps that are irreconcilable with the observations. This conclusion is qualitatively insensitive to the matter content of the universe, in particular, the presence of a cosmological constant. If the universe is of comparable size to the 'horizon', the likelihood function is very dependent upon orientation of the manifold wrt the sky. While most orientations may be strongly ruled out, it sometimes happens that for a specific orientation the predicted correlation patterns are preferred over those for the conventional infinite models. The full Bayesian analysis we use is the most complete statistical test that can be done on the COBE maps, taking into account all possible signals and their variances in the theoretical skies, in particular the high degree of anisotropic correlation that can exist. We show that standard visual measures for comparing theoretical predictions with the data such as the isotropized power spectrum $C_\ell$ are not so useful in small compact spaces because of enhanced cosmic variance associated with the breakdown of statistical isotropy.