发表机构
Chongqing University of Science and Technology; Zhengzhou University; Chongqing University of Posts & Telecommunications; Chongqing University（重庆科技大学; 郑州大学; 重庆邮电大学; 重庆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究构造了超出慢滚近似的单场暴胀精确解，分析其吸引子与演化，结合CMB似然找到兼容参数区，数值验证了解的预测精度，拓展了暴胀理论的适用范围。
AI 中文摘要
我们构造了无需借助慢滚近似的单场暴胀子动力学的精确解。合适的变量变换将背景方程约化为第一类阿贝尔方程。尽管一般的阿贝尔方程无法解析求解，我们仍识别出一类暴胀子势，其变换后的方程存在精确解。所得框架包含常滚暴胀作为特例，也可容纳具有二阶哈勃流参数恒定的解。我们分析了这些滚动背景的线性局域吸引子行为与超视界演化。利用$(n_s,r)$平面内公开的联合CMB似然轮廓，我们识别出兼容的参数区域，并表明某一滚动分支也可给出$50\leq N_*<60$。在代表点处对标量与张量模式的直接数值演化验证了局域指数预测，其在$n_s$上的精度优于$7\times10^{-4}$，在$r$上优于$2\times10^{-6}$。该精确族延伸至慢滚之外，尽管本文展示的观测选定区域靠近慢滚 regime。
英文摘要
We construct exact solutions for single-field inflaton dynamics without invoking the slow-roll approximation. A suitable change of variables reduces the background equation to an Abel equation of the first kind. Although a generic Abel equation is not analytically solvable, we identify a class of inflaton potentials for which the transformed equation admits exact solutions. The resulting framework contains constant-roll inflation as a special case and also accommodates solutions with a constant second Hubble-flow parameter. We analyze the linear local attractor behavior and superhorizon evolution of these rolling backgrounds. Using the public joint CMB likelihood contours in the $(n_s,r)$ plane, we identify compatible parameter regions and show that one rolling branch can also yield $50\leq N_*<60$. Direct numerical evolution of the scalar and tensor modes at representative points validates the local-index predictions to better than $7\times10^{-4}$ in $n_s$ and $2\times10^{-6}$ in $r$. The exact family extends beyond slow roll, although the observationally selected regions displayed here lie close to the slow-roll regime.
Comments26pages,5 figures
