可精确积分的ΛCDM模拟f(Q)宇宙学：第一联络分支中的背景、稳定性与扰动
Exact Integrable $Λ$CDM-Mimicking $f(Q)$ Cosmology: Background, Stability, and Perturbations in the First Connection Branch
- Department of Mathematics, St. Anthony’s College（圣安东尼学院数学系）
- SGT University（SGT大学）
- Centre For Cosmology and Science Popularization (CCSP), SGT University（宇宙学与科学普及中心（CCSP），SGT大学）
- Institute of Research and Development, Duy Tan University（得台大学研发院）
- Faculty of Natural Sciences, Duy Tan University（得台大学自然科学学院）
- Center for Space Research, North-West University（西北大学太空研究中心）
- Mathematics Division, Department of Basic Sciences and Social Sciences, North Eastern Hill University（东北山大学基础科学与社会科学系数学分部）
- Inter University Centre for Astronomy and Astrophysics（大学间天文与天体物理中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文在f(Q)引力第一联络分支中，通过宇宙学闭合策略等方法获得ΛCDM模拟f(Q)模型的可积分动力学解，分析其稳定性并与f(R)引力对应动力学比较，为研究相关宇宙学动力学提供系统途径。
AI中文摘要：
我们在f(Q)引力的第一联络分支框架内，重新研究模拟标准宇宙学模型（其特征为j=1，其中j为宇宙学加加速度参数）的问题。虽然该问题此前已通过重构技术解决，得到解析形式f(Q)=-2Λ+αQ+β√(-Q)（其中Q=-6H²），但本文从两个不同视角处理该问题：对传统动力学系统公式应用宇宙学闭合策略或辅助变量层级方法。值得注意的是，宇宙学闭合使ΛCDM模拟f(Q)模型的动力学系统可积分，因此我们获得了所有相关宇宙学量在背景和线性扰动层面的闭式解析解，扰动解以广义Heun函数优雅表达。此外，我们分析了ΛCDM模拟相空间对j=1的小运动学偏差的结构稳定性，证明了这些解的鲁棒性。本文方法为研究ΛCDM模拟动力学提供了系统途径，无需对基础作用量进行闭式解析重构。最后，我们利用该框架建立了f(Q)引力第一联络分支中ΛCDM模拟动力学与f(R)引力中对应动力学的直接比较。
英文摘要：
We re-examine the problem of mimicking the standard cosmological model, characterized by $j=1$ (where $j$ is the cosmographic jerk parameter), within the context of the first connection branch of $f(Q)$ gravity. While this problem has previously been addressed via reconstruction techniques$-$yielding the analytic form $f(Q)=-2Λ+αQ + β\sqrt{-Q}$ with $Q=-6H^2$ $-$here we tackle this problem from two distinct perspectives, applying either a cosmographic closure strategy or an auxiliary-variable hierarchy approach to the traditional dynamical systems formulation. Remarkably, the cosmographic closure renders the dynamical system integrable for $Λ$CDM-mimicking $f(Q)$ models. Consequently, we obtain closed-form analytical solutions for all relevant cosmological quantities at both the background and linear perturbation levels, with the perturbative solutions elegantly expressed in terms of generalized Heun functions. Furthermore, we analyze the structural stability of the $Λ$CDM-mimicking phase space against small kinematic deviations from $j=1$, demonstrating the robustness of these solutions. Our approach provides a systematic route to studying $Λ$CDM-mimicking dynamics without requiring a closed-form analytic reconstruction of the underlying action. Finally, we utilize this framework to establish a direct comparison between $Λ$CDM-mimicking dynamics in the first connection branch of $f(Q)$ gravity and those in $f(R)$ gravity.
