正则宇宙学：三条不同路径
Regular Cosmologies: Three Distinct Routes
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中文总结 AI 辅助
本研究探讨将正则黑洞的德西特核心思想应用于早期宇宙，通过三种方案（牛顿、随动真空、准局域）分析六个正则度规，发现核心密度单调递减时状态方程不跨越w=-1，且单一正则化长度无法同时解释暴胀与暗能量。
中文摘要 AI 辅助
正则黑洞通过用德西特核心取代中心奇点来避免奇点。我们提出疑问：如果将同样的想法应用于早期宇宙，会得到什么样的宇宙学。正则度规定义了一个依赖于位置的宇宙学术语，$\Lambda_{\rm eff}(r)=8\pi G \rho_{\rm MS}(r)$，并且没有唯一的方法将其推广到膨胀的宇宙。我们遵循三种不同的方案：一种遵循麦科里亚和米尔恩的牛顿方案，一种在哈勃半径处评估的随动真空方案，以及一种基于米斯纳-夏普质量的准局域方案。我们将每种方案应用于六个正则黑洞度规，并探讨其后果。在牛顿情形下，弗里德曼方程对海沃德度规以闭式形式求解，对其他度规则以标准特殊函数或数值形式求解，并描述了一个从德西特相开始、以尘埃结束的宇宙（即一个暴胀模型而非暗能量）。我们发现，在所有三种方案中，单调递减的核心密度给出的状态方程从不跨越$w=-1$，因此DESI所暗示的幻影行为需要一个密度壳层，而正则核心并不具备。三种方案在德西特核心上一致，但在晚期有所不同，我们针对DESI DR2结果量化了这一差异。我们还指出，单一的正则化长度不能同时充当暴胀尺度和暗能量尺度。
英文摘要
Regular black holes avoid the central singularity by replacing it with a de Sitter core. We ask what cosmology follows if the same idea is brought to the early universe. Regular metrics define a position-dependent cosmological term, $Λ_{\rm eff}(r)=8πG ρ_{\rm MS}(r)$, and there is no unique way to carry it over to the expanding universe. We follow three different prescriptions: a Newtonian one following McCrea and Milne, a running vacuum evaluated at Hubble radius and a quasi-local one based on Misner-Sharp mass. We apply each of them to six regular black hole metrics and explore their consequences. In the Newtonian case the Friedmann equations are solved in closed form for the Hayward metric, and in terms of standard special functions or numerically for the others, and describe a universe that starts in a de Sitter phase and ends as dust (i.e. an inflationary model instead of dark energy). We find that in all three prescriptions a monotonically decreasing core density gives an equation of state that never crosses $w=-1$, and thus the phantom behaviour suggested by DESI would require a density shell which a regular core does not have. The three prescriptions agree on the de Sitter core but differ at late times, and we quantify the difference against the DESI DR2 results. We also point out that a single regularisation length cannot serve as both the inflationary and the dark-energy scale.
发表机构
- Pontificia Universidad Javeriana（波哥大耶稣会天主教大学）
- ICTP–South American Institute for Fundamental Research（国际理论物理中心南美基础研究所）
- Universidade Federal de São Paulo (UNIFESP)（圣保罗联邦大学）
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