用LTB模型探测空间均匀性：详细讨论
Probing spatial homogeneity with LTB models: a detailed discussion
摘要：
目前的观测数据是否证实了宇宙学原理的假设，或者是否有统计学证据表明大尺度上的空间均匀性存在偏差？为了解决这些问题，我们开发了一个灵活的框架的基础上球对称，但径向不均匀的Lemaitre-Tolman-Bondi（LTB）模型与同步大爆炸。我们扩大了（本地）物质密度分布的灵活的插值方案和正交多项式。蒙特卡洛技术与最近的观测数据相结合，被用来系统地改变这些配置文件的形状。在这篇文章的第一部分，我们重新考虑巨大的LTB空洞没有暗能量，以调查是否极其微调的质量分布可以调和这些模型与当前的数据。虽然局部哈勃率和超新星可以很容易地在没有暗能量的情况下拟合，但是，普朗克2013年数据的模型独立约束要求不切实际的低局部哈勃率，这与观测值强烈不一致;这个结果与以前的研究吻合得很好。在第二部分中，我们解释了为什么用一个非零的宇宙学常数来扩展我们的框架似乎是很自然的，这使我们能够对宇宙学原理进行一般性的检验。此外，这些扩展的模型有助于探索是否在当地的物质密度分布的波动可能会缓解哈勃率的本地和全球测量之间的紧张局势，来自造父变星校准的Ia型超新星和CMB实验，分别。我们发现，目前的数据提供了大尺度上的空间均匀性偏差的证据。然而，要最终确认宇宙学原理的有效性，还需要更精确的约束。
英文摘要：
Do current observational data confirm the assumptions of the cosmological principle, or is there statistical evidence for deviations from spatial homogeneity on large scales? To address these questions, we developed a flexible framework based on spherically symmetric, but radially inhomogeneous Lemaitre-Tolman-Bondi (LTB) models with synchronous Big Bang. We expanded the (local) matter density profile in terms of flexible interpolation schemes and orthonormal polynomials. A Monte Carlo technique in combination with recent observational data was used to systematically vary the shape of these profiles. In the first part of this article, we reconsider giant LTB voids without dark energy to investigate whether extremely fine-tuned mass profiles can reconcile these models with current data. While the local Hubble rate and supernovae can easily be fitted without dark energy, however, model-independent constraints from the Planck 2013 data require an unrealistically low local Hubble rate, which is strongly inconsistent with the observed value; this result agrees well with previous studies. In the second part, we explain why it seems natural to extend our framework by a non-zero cosmological constant, which then allows us to perform general tests of the cosmological principle. Moreover, these extended models facilitate explorating whether fluctuations in the local matter density profile might potentially alleviate the tension between local and global measurements of the Hubble rate, as derived from Cepheid-calibrated type Ia supernovae and CMB experiments, respectively. We show that current data provide no evidence for deviations from spatial homogeneity on large scales. More accurate constraints are required to ultimately confirm the validity of the cosmological principle, however.
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