A 2.29 GHz VLBI all-sky survey of ultra-compact radio sources has formed the basis of a number of cosmological investigations, which examine the relationship between angular-size and redshift. Here I use a sample of 468 such sources with 0.5<z<=3.787, to investigate the isotropy of the Universe. The sample is divided into hemispherical sub-samples, over an all-sky 5 degree x 5 degree array, each of which is allowed to determine a value of Omega_m, assuming that we are living in a spatially flat homogeneous isotropic LambdaCDM model. If we regard the latter as a null hypothesis, then it fails the test -- the results show significant anisotropy, the smallest value of Omega_m being towards (l,b)=(253.9,24.1) degrees, the largest in the opposite direction. This is close to the CMB dipole axis, but in the obverse sense. This is interpreted as meaning that the Universe is not spatially homogeneous on the largest scales, and is better represented at late times by a spherically symmetric model with a density enhancement at its centre.
Testing cosmic homogeneity and isotropy using galaxy correlations
尽管它在宇宙学中具有根本的重要性，但很少有直接的宇宙学原理测试。由于普朗克合作小组最近观测到的宇宙微波背景中存在半球不对称性，这样的测试特别及时。迄今为止，大多数测试都着眼于宇宙学参数的红移依赖性。这些都受到大的系统性影响，需要建模和偏差校正。与以前的测试不同，这里描述的测试比较了相同红移z下等体积的星系分布。这允许直接测试，并且z依赖的偏差不是问题。使用SDSS DR 7巡天中的~10^6个星系，我证明了相隔~2 Gpc的空间区域具有相同的平均星系相关半径、振幅和数密度，其范围约为2 Gpc。5%，与标准模型预期一致。
A measurement of the scale of homogeneity in the Early Universe
我们提出的均匀性指数，$\mathcal{H}$，早期宇宙的分形或Hausdorff维数的普朗克宇宙微波背景温度变化$δT$在天空中的第一个测量。各向同性尺度的这种表征是无模型的并且是纯几何的，与$δT$的振幅无关。我们发现证据的均匀性（$\mathcal{H}=0$）的尺度大于$θ_{\mathcal{H}} = 65.9 \pm 9.2 °$的CMB天空。这一发现与$Λ$ CDM预测不一致，后者假设宇宙是尺度不变的。这种异常与角$δT$谱中众所周知的低四极振幅一致，但以直接和模型独立的方式进行量化。我们估计的意义，我们发现$\mathcal{H}=0$使用主成分分析从观测天空的采样变化。假设平移不变性（和平坦几何），我们可以将各向同性尺度$θ_\mathcal{H}$转换成（共动）均匀尺度，这是非常接近所观察到的宇宙学常数$Λ$产生的陷阱表面的协方差矩阵\textcolor{black}{ and simulations, booth base purely on data or in the $Λ$CDM prediction.}的理论预测验证分析。
Testing the cosmological principle on gigaparsec scales
School of Physics and Astronomy, Sun Yat-sen University（中山大学物理学院）；CSST Science Center for the Guangdong-Hongkong-Macau Greater Bay Area,Sun Yat-sen University（中山大学粤港澳大湾区空间站科学中心）
Measurements of the Angular Homogeneity Scale from DESI DR1
Observatório Nacional（国家天文台）；Universidade Federal Rural do Rio de Janeiro（里约热内卢联邦农村大学）；Zhejiang University（浙江大学）；Universidade do Estado do Rio de Janeiro（里约热内卢州立大学）
