发表机构
Indian Institute of Technology Kanpur（坎普尔印度理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出一个膜世界循环宇宙模型，通过动力学耦合熵场解决反弹奇异性、蓝倾斜和熵积累问题，匹配观测谱指数并确定相关参数。
AI 中文摘要
循环宇宙学用永恒的平滑转折序列取代了暴胀的单一创生事件，但历史上存在三个问题阻碍了其发展：奇异性反弹、单场反弹收缩中普遍存在的蓝倾斜，以及托尔曼关于熵产生应使连续循环无界地变得更长更大的观测。我们在一个显式模型中解决了所有这三个问题。具有类时额外维度的兰德尔-桑德鲁姆膜在不违反零能量条件的情况下规范了反弹，单个标量场的势能将宇宙从解冻暗能量高原通过变号转折带入BKL安全的反弹收缩并返回。我们证明，膜弗里德曼方程内部的任何修正以及任何直线双场轨迹都无法将谱指数从普遍的反弹结果$n_s\approx3$中拯救出来。然后我们构建了能够做到这一点的最小完备方案：一个动力学耦合的熵场，遵循伊贾斯、莱纳和斯坦哈特的一般机制，其耦合陡度对于该模型的反弹势具有闭式精确尺度不变值，仅需百分之一级别的偏移即可匹配测量到的倾斜$n_s=0.9649$。这确定了局部非高斯性（$f_{\rm NL}\approx-0.02$）和张量标量比（$r\approx7.6\times10^{-26}$）。匹配观测到的振幅将转换耦合和膜张力确定为平常值（$\lambda\approx5.7\times10^{-3}$，$\rho_c^{1/4}=10^{13}\\,$GeV）。最后，由于膜构造是空间平坦的，托尔曼熵论证在此并不限制循环次数：我们推导出每次循环需要约70-80个e折的加速膨胀，以在下次收缩前将产生的熵稀释回可忽略的密度。
英文摘要
Cyclic cosmologies replace inflation's single creation event with an eternal sequence of smooth turnarounds, but three problems have historically stood in their way: singular bounces, the blue tilt generic to single-field ekpyrotic contraction, and Tolman's observation that entropy production should make successive cycles longer and larger without bound. We resolve all three within one explicit model. A Randall-Sundrum brane with a timelike extra dimension regularizes the bounce without violating the null energy condition, and a single scalar field's potential carries the universe from a thawing dark-energy plateau through a sign-changing turnaround into a BKL-safe ekpyrotic contraction and back. We show that no correction internal to the brane's Friedmann equation, and no straight two-field trajectory, can rescue the spectral index from the generic ekpyrotic result $n_s\approx3$. We then build the minimal completion that can: a kinetically coupled entropy field, following the general mechanism of Ijjas, Lehners, and Steinhardt, whose coupling steepness has a closed-form, exact-scale-invariance value for this model's ekpyrotic potential, with only a percent-level offset needed to match the measured tilt $n_s=0.9649$. This fixes the local non-Gaussianity ($f_{\rm NL}\approx-0.02$) and tensor-to-scalar ratio ($r\approx7.6\times10^{-26}$). Matching the observed amplitude fixes the conversion coupling and brane tension to unremarkable values ($λ\approx5.7\times10^{-3}$, $ρ_c^{1/4}=10^{13}\,$GeV). Finally, because the brane construction is spatially flat, Tolman's entropy argument does not bound the number of cycles here: we derive $N_{\rm DE}\sim70$-80 e-folds of accelerated expansion needed each cycle to dilute the entropy produced back to a negligible density before the next contraction.
