AI 中文总结
研究原初宇宙中含非最小耦合\(-\xi\phi^2 R\)的暴胀模型，在约旦框架分析其对\(r\)和\(n_s\)的观测预测。发现负\(\xi\)对\(r\)和\(n_s\)有特定影响，四次模型与ACT DR6数据相符，能统一解释CMB约束。
AI 中文摘要
引力与暴胀场之间的非最小耦合是暴胀宇宙学中的一个普遍贡献。在这项工作中，我们考虑具有非最小耦合\(-\xi\phi^2 R\)的暴胀模型，并研究它们对标量张量比\(r\)和谱指数\(n_s\)的观测预测。与在爱因斯坦框架中工作的传统方法不同，我们在约旦框架中进行分析，其中潜在动力学，特别是势能力与耦合诱导摩擦之间的竞争更加透明。对于合适的\(\xi\)值，系统表现出扩展的常滚 regime，其中这种摩擦抵消了势能力。专注于单项式势\(V(\phi) \propto \phi^n\)，我们发现负\(\xi\)在\((n_s, r)\)平面中系统地降低\(r\)，而\(n_s\)的变化取决于幂\(n\)：对于\(n \geq 4\)，谱指数随\(|\xi|\)增加，而对于\(n < 4\)，它减小。值得注意的是，\(\xi \lesssim -0.1\)的四次模型\(V(\phi) = \lambda \phi^4/4\)与ACT DR6数据显示出良好的一致性，并且与其他单项式情况相比表现出明显的\(n_s(\xi)\)依赖性。我们的结果表明，非最小耦合模型可以有效地协调普朗克和ACT观测，为解释当前的CMB约束提供了一个统一的框架。
英文摘要
A non-minimal coupling between gravity and the inflaton field is a generic contribution in inflationary cosmology. In this work, we consider models of inflation with a non-minimal coupling $-ξϕ^2 R$ and study their observational predictions for the tensor-to-scalar ratio $r$ and the spectral index $n_s$. Unlike the conventional approach of working in the Einstein frame, we perform the analysis in the Jordan frame where the underlying dynamics, particularly the competition between the potential force and the coupling-induced friction, are more transparent. For suitable values of $ξ$, the system exhibits an extended constant-roll regime, in which this friction counteracts the potential force. Focusing on monomial potentials $V(ϕ) \propto ϕ^n$, we find that negative $ξ$ systematically reduces $r$ in the $(n_s, r)$ plane, while the shift in $n_s$ depends on the power $n$: for $n \geq 4$, the spectral index increases with $|ξ|$, whereas for $n < 4$, it decreases. Notably, the quartic model $V(ϕ) = λϕ^4/4$ with $ξ\lesssim -0.1$ shows good agreement with the ACT DR6 data and exhibits a distinct $n_s(ξ)$ dependence compared to other monomial cases. Our results demonstrate that non-minimally coupled models can effectively reconcile Planck and ACT observations, providing a unified framework for interpreting current CMB constraints.
Comments24 pages, 7 figures
