AI 中文总结
本文提出多时期停滞梳的解析模板，用于在暴胀引力波背景中识别循环宇宙学停滞特征，并验证其作为区分恒定状态方程模型的强判别器。
AI 中文摘要
宇宙学停滞可以多次复发，每一次发生都会在暴胀引力波背景（IGWB）上留下一个特征印记。我们将单时期谱模板扩展到任意数量 $N$ 个连续停滞时期，推导出一个闭式的 $N$ 时期分段模板，该模板可以干净地分解：每个断点处的振幅阶跃完全由该时期的局部状态方程 $w_s^{(i)}$ 决定，而时期之间的平台水平则编码了来自所有先前时期的累积谱倾斜。每个可分辨的谱特征都提供了对 Bessel 函数一致性关系 $C^2 = C^2(\alpha)$（在~\cite{BarenboimBurns:paper1} 中建立）的独立检验，而 $N$ 个这样的检验同时被一个非停滞谱满足的概率随 $N$ 急剧下降，使得一个确认的多时期梳成为对抗恒定 $w$ 替代模型的最强判别器。我们将该形式应用于~\cite{Dienes:2023ziv} 的三重停滞场景，该场景依次串联了三个成对的停滞机制（物质/辐射、真空能/物质、真空能/辐射）。对于每个块，我们推导出该时期位于模板有效范围 $w_s > -1/3$ 内的条件。我们表明~\cite{Dienes:2023ziv} 的 Fig.~3 基准落在此范围之外，并确定了既物理可实现又可供模板访问的参数选择。我们针对代表性的两块和三块链数值验证了平台间比率预测，并研究了相邻时期共享断点频率而无中间辐射主导区间的接触时期极限。最后，我们讨论了各种多时期停滞场景的可探测性，并给出了最小可探测张标比作为循环停滞时期数量的函数。
英文摘要
Cosmological stasis can recur multiple times, and each occurrence imprints a characteristic feature on the inflationary gravitational wave background (IGWB). We extend the single-epoch spectral template to an arbitrary number $N$ of consecutive stasis epochs, deriving a closed-form $N$-epoch piecewise template that factorizes cleanly: the amplitude steps at each break are determined entirely by the local equation of state $w_s^{(i)}$ of that epoch, while the inter-epoch plateau levels encode the accumulated spectral tilt from all prior epochs. Each resolved spectral feature yields an independent test of the Bessel-function consistency relation $C^2 = C^2(α)$ established in~\cite{BarenboimBurns:paper1}, and the probability that $N$ such tests are simultaneously satisfied by a non-stasis spectrum falls sharply with $N$, making a confirmed multi-epoch comb the strongest available discriminator against constant-$w$ alternatives. We apply the formalism to the triple-stasis scenario of~\cite{Dienes:2023ziv}, which chains three pairwise stasis mechanisms (matter/radiation, vacuum-energy/matter, vacuum-energy/radiation) sequentially. For each block we derive the conditions under which the epoch lies within the template's validity range $w_s > -1/3$. We show that the Fig.~3 benchmark of~\cite{Dienes:2023ziv} falls outside this range and identify parameter choices that are both physically realizable and accessible to the template. We validate the inter-plateau ratio predictions numerically for representative two- and three-block chains, and work out the touching-epoch limit in which consecutive blocks share a break frequency without an intervening radiation-dominated interval. Finally, we discuss the detectability of a variety of multi-epoch stasis scenarios and give the minimum detectable tensor-to-scalar ratio as a function of the number of recurrent stasis epochs.
Comments24 pages, 6 figures
