宇宙拓扑。第 Va 部分。可观测宇宙的信息含量

本文探讨了若宇宙具有紧致空间拓扑结构，其对称性变换如何在密度扰动中留下统计相关性。研究通过计算可观测子体积内的模协方差，评估了线性扰动中蕴含的拓扑信息。结果表明，利用三维宇宙密度场探测拓扑的范围，可比仅使用宇宙微波背景各向异性提升 25%。

arXiv:2608.25033v1 Announce Type: new Abstract: If the Universe possesses a compact spatial topology with characteristic scale not much larger than the diameter of the observable Universe, then the associated symmetry transformations imprint specific statistical correlations on density perturbations. We derive the covariance between perturbation modes in the full topology volume and compute the induced covariance between modes in the observable subvolume. We then use this covariance to estimate the available information about topology contained in the full set of observable linear perturbations. For two sample Euclidean examples - the cubic three-torus ($E_1$) and a three-torus with a quarter turn ($E_3$) - the three-dimensional density field carries enough information to detect topology on scales up to 25 percent larger than those accessible from the two-dimensional cosmic microwave background anisotropies alone. Future probes of the cosmic density field using deep galaxy surveys or neutral-hydrogen 21-cm intensity mapping, combined with computationally intensive searches over the large parameter space of admissible topologies, thus offer a plausible avenue to extending the range of detectable cosmic topologies.