宇宙空间曲率和均匀性的新零检验及其机器学习重建
Novel null tests for the spatial curvature and homogeneity of the Universe and their machine learning reconstructions
摘要：
在过去的几十年中获得的大量观测数据使宇宙学进入了一个精确的时代，并导致了标准宇宙学常数和冷暗物质范式的基础，称为$Λ$ CDM模型。考虑到这种一致性模型的许多可能的扩展，我们在这里提出了几个新的一致性测试，可用于探测偏离$Λ$ CDM。首先，我们推导出一个联合一致性检验的空间曲率$Ω_{k,0}$和物质密度$Ω_\textrm{m,0}$参数，只使用哈勃率$H(z)$，这可以直接从观测确定。其次，我们提出了一个新的测试可能偏离均匀性使用两个数据集的组合，无论是重子声学振荡（BAO）和$H(z)$数据或横向和径向的BAO数据，而我们也介绍了两个一致性测试$Λ$ CDM可以通过横向和径向BAO数据重建。然后，我们使用特定的机器学习方法，即遗传算法，以独立于模型的方式使用当前可用的数据重建上述测试。最后，我们还报告了一个$\sim 4σ$张力的过渡红移所确定的$H(z)$和径向BAO数据。
英文摘要：
A plethora of observational data obtained over the last couple of decades has allowed cosmology to enter into a precision era and has led to the foundation of the standard cosmological constant and cold dark matter paradigm, known as the $Λ$CDM model. Given the many possible extensions of this concordance model, we present here several novel consistency tests which could be used to probe for deviations from $Λ$CDM. First, we derive a joint consistency test for the spatial curvature $Ω_{k,0}$ and the matter density $Ω_\textrm{m,0}$ parameters, constructed using only the Hubble rate $H(z)$, which can be determined directly from observations. Second, we present a new test of possible deviations from homogeneity using the combination of two datasets, either the baryon acoustic oscillation (BAO) and $H(z)$ data or the transversal and radial BAO data, while we also introduce two consistency tests for $Λ$CDM which could be reconstructed via the transversal and radial BAO data. We then reconstruct the aforementioned tests using the currently available data in a model independent manner using a particular machine learning approach, namely the Genetic Algorithms. Finally, we also report on a $\sim 4σ$ tension on the transition redshift as determined by the $H(z)$ and radial BAO data.
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