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arXiv 2408.15166hep-thgr-qc
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黑洞-de Sitter模型，关于de Sitter相的一个提议

Black hole-de Sitter model, a proposal for the de Sitter phases

Ida M. Rasulian

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10 pages
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AI总结：

本文扩展了膜世界-黑洞de Sitter模型，通过非微扰方法研究膜上的有效引力，发现膜上有效宇宙学常数的演化取决于体中流向和流出黑洞的能量通量，并指出该模型可描述低尺度暴胀相与晚期暗能量相之间的过渡。

摘要：

我们扩展了在\cite{Rasulian}中引入的膜世界-黑洞de Sitter模型，该模型是一个用于构建有效de Sitter时空的提议，且不显式依赖于膜张力或体宇宙学常数。在此模型中，4D de Sitter空间涌现于5D黑洞视界附近的一条膜上。我们采用近似Z2对称性假设，非微扰地研究了膜上的有效引力（至多相差一个共形因子），并发现膜上有效宇宙学常数的演化取决于体中流向和流出黑洞的能量通量。在此设置中，黑洞视界的存在为膜的演化设定了初始条件，且一旦视界形成，膜便接近其具有de Sitter长度$l\lesssim l_5$（其中$l_5$为5D Planck长度）的零位形。在跟随该阶段的坍缩最后阶段（或视界形成后体中物质的进一步通量）中，膜上的有效de Sitter长度由于下落通量而相对快速地增加。这一阶段暂时是低尺度暴胀相与晚期暗能量相之间的过渡。我们还观察到，de Sitter长度的增加伴随着由于跨膜体通量跃变而进入膜的能量通量。考虑到膜的初始状态处于视界的$l_5$邻域内，略低于视界的位形是AdS半径为$l\lesssim l_5$的Euclidean AdS。这可以被解释为所得宇宙学的一个边界提议。

英文摘要：

We expand on the braneworld-black hole de Sitter model introduced in \cite{Rasulian} which is a proposal for constructing an effective de Sitter spacetime with no explicit dependence on brane tension or bulk cosmological constant. In this model the 4D de Sitter space emerges on a brane near the horizon of a 5D black hole. We study the effective gravity on the brane non-perturbatively, with an approximate Z2 symmetry assumption, up to a conformal factor, and find that the evolution of the effective cosmological constant on the brane depends on the flux of energy towards and away from the black hole in the bulk. In this setup the presence of the black hole horizon sets the initial condition for the brane's evolution and the brane approaches its null configuration with de Sitter length $l\lesssim l_5$, where $l_5$ is the 5D Planck's length, as soon as the horizon forms. During the last stages of collapse following this phase (or further flux of matter in the bulk after the horizon is formed), the effective de Sitter length on the brane increases due to the in-falling flux relatively fast. This phase is tentatively the transition between a low scale inflationary phase and the late dark energy phase. Also we observe that the increase in the de Sitter length is accompanied with a flux of energy entering the brane due to the jump in the bulk flux across the brane. Considering the initial state of the brane to be in the $l_5$ neighborhood of the horizon, the configuration which is slightly below the horizon is Euclidean AdS with AdS radius $l\lesssim l_5$. This can be interpreted as a boundary proposal for the resulting cosmology.

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