高标度下的非最小耦合链暴胀
Non-Minimally Coupled Chain Inflation at High Scales
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中文总结 AI 辅助
该研究探讨高标度下非最小耦合对链暴胀的影响，建立关联隧穿动力学与原初可观测信号的解析框架，实现高标度链暴胀并预言可探测的随机引力波与谱指数跑动。
中文摘要 AI 辅助
链暴胀为标准慢滚动力学提供了一种替代方案，其加速膨胀是通过亚稳真空之间一系列快速的量子隧穿事件实现的。与早期宇宙相关的高能标下，标量场通常会通过ξRφ²这类算符与引力发生非最小耦合，这类耦合由对称性允许，也是弯曲时空中相互作用理论抵消项所要求的。我们研究了这种耦合对链暴胀的动力学和观测后果，分析了任意ξ值下的模型修正，并重点关注ξ为O(10)时的有趣现象学。我们证明，在爱因斯坦框架下，非最小耦合会诱导出依赖于场的欧几里得 bounce 作用量放大，从而改变链中的隧穿率。我们建立了一个解析框架，将这种修正后的隧穿动力学与标量谱指数、其跑动、原初曲率功率谱以及气泡碰撞产生的随机引力波背景关联起来。作为一个结果，非最小耦合打破了标量倾斜与暴胀标度之间的刚性关系——该关系会使最小耦合的纯倾斜余弦模型走向极低能标（V_*^(1/4)≲3 GeV，其中V_*是与CMB相关的模式出视界时暴胀势的取值），从而允许存在V_*^(1/4)~10¹¹ GeV的可行高标度链暴胀。此外，高标度下的非最小耦合链暴胀会在毫赫兹至千赫兹频段产生一个峰值随机引力波信号，该信号可被爱因斯坦望远镜（Einstein Telescope）和宇宙探测器（Cosmic Explorer）等即将建成的干涉仪探测到。最后，该模型预言了一个可被西蒙斯天文台（Simons Observatory）检验的独特谱指数跑动，使其成为多信使宇宙学的主要研究目标。
英文摘要
Chain inflation offers an alternative to standard slow-roll dynamics, with accelerated expansion proceeding through a sequence of rapid quantum tunneling events between metastable vacua. At the high energy scales relevant for the early Universe, scalar fields are generically expected to couple non-minimally to gravity via operators like $ξRϕ^2$, allowed by symmetry and required as counterterms for interacting theories in curved spacetime. We study the dynamical and observational consequences of this coupling for chain inflation. We find the modifications to the model for arbitrary $ξ$ and focus on interesting phenomenology for $ξ={\cal O}( 10)$. We show that, in the Einstein frame, the non-minimal coupling induces a field-dependent amplification of the Euclidean bounce action, thus modifying the tunneling rate across the chain. We develop an analytic framework connecting this modified tunneling dynamics to the scalar spectral index, its running, the primordial curvature power spectrum, and the stochastic gravitational wave background from bubble collisions. As one consequence, the non-minimal coupling breaks the rigid relation between the scalar tilt and inflationary scale that drives the minimally coupled pure tilted cosine model to very low energies ($V_*^{1/4}\lesssim 3\,\rm{GeV}$, where $V_*$ is the value of the inflationary potential when the CMB-relevant modes exit the horizon), allowing for viable high-scale chain inflation with $V_*^{1/4}\sim 10^{11}\,\rm{GeV}$. Furthermore, non-minimally coupled chain inflation at high scales produces a peaked stochastic gravitational wave signal in the dHz-kHz bands, accessible to upcoming interferometers such as the Einstein Telescope and Cosmic Explorer. Finally, the model predicts a distinct running of the spectral index that will be testable by the Simons Observatory, making it a prime target for multi-messenger cosmology.
