标题： 揭示类星体分布中大尺度宇宙各向异性的过渡时期 显示英文标题

标题： Revealing a transitional epoch of large-scale cosmic anisotropy in the quasar distribution

摘要： 宇宙学原理认为，在最大的尺度上，宇宙是各向同性的。 虽然这一基本假设得到了广泛支持，但仍然是可检验的。 我们使用瑞尼熵（Renyi entropy），一种对高阶聚类敏感的多尺度统计量，分析了来自Gaia-unWISE目录中超过一百万个类星体的角度分布。 将样本分为三个红移区间，我们发现低红移和高红移的分布在统计上与各向同性一致。 然而，在中间红移（$1 \leq z < 2.2$）处，我们检测到一个统计显著且与尺度相关的各向异性，即使在严格的遮蔽条件下仍然存在，这表明其具有物理起源。 我们将其解释为宇宙历史中过渡时期的证据，在此期间，如超星系团这样的大尺度结构变得显著，但在加速膨胀开始后，它们的增长逐渐被抑制。 这些发现使瑞尼熵成为研究宇宙演化的有力探针，并突显了结构形成、熵耗散与大尺度各向同性出现之间潜在的热力学联系。 显示英文摘要

摘要： The Cosmological Principle posits that the Universe is isotropic on the largest scales. While widely supported, this foundational assumption remains testable. We analyse the angular distribution of over one million quasars from the Gaia-unWISE catalogue using Renyi entropy, a multiscale statistical measure sensitive to higher-order clustering. Dividing the sample into three redshift bins, we find that both the low- and high-redshift distributions are statistically consistent with isotropy. However, at intermediate redshift ($1 \leq z < 2.2$), we detect a statistically significant and scale-dependent anisotropy that persists under stringent masking, suggesting a physical origin. We interpret this as evidence for a transitional epoch in cosmic history, during which large-scale structures such as superclusters became prominent before their growth was gradually damped by the onset of accelerated expansion. These findings position Renyi entropy as a powerful probe of cosmic evolution and highlight the potential thermodynamic links between structure formation, entropy dissipation, and the emergence of large-scale isotropy.