从测地线汇动力学重建 $f(Q)$ 引力：Raychaudhuri 方程
Reconstruction of $f(Q)$ Gravity from Geodesic Congruence Dynamics: Raychaudhuri Equation
浏览论文内容
中文总结 AI 辅助
本研究利用Raychaudhuri方程作为几何工具，在对称遥平行引力框架下重建$f(Q)$引力函数形式，所得模型无需暗能量即可解释宇宙加速膨胀，并可作为逆重建的中心方程。
中文摘要 AI 辅助
在本研究中，我们利用 Raychaudhuri 方程作为基本的几何工具，在对称遥平行引力的背景下重建 $f(Q)$ 引力的函数形式。利用 Raychaudhuri 方程中记录的膨胀标量和汇动力学，将非度规标量 $Q$ 与宇宙的运动学演化联系起来，以建立重建方法。通过考虑适当的宇宙学假设，我们得到了 $f(Q)$ 的显式形式，这些形式可以解释观测到的宇宙加速膨胀，而无需额外的暗能量成分。此外，重建的模型还可以扩展到无限过去，以模拟某些情景下的早期宇宙。在 FLRW 时空中，我们考虑了恒定的减速参数和恒定的加加速度参数，以促进我们的重建分析。我们进一步讨论了重建模型的广义相对论极限、Friedmann 一致性以及背景物理可行性。分析表明，Raychaudhuri 方程被解释为控制宇宙学测地线汇聚焦/散焦的方程，可以用作 $f(Q)$ 引力逆重建的中心方程。
英文摘要
In this study, we use the Raychaudhuri equation as the essential geometrical tool to reconstruct the functional form of $f(Q)$ gravity within the context of symmetric teleparallel gravity. The expansion scalar and the congruence dynamics recorded in the Raychaudhuri equation are used to relate the non-metricity scalar $Q$ with the kinematical evolution of the Universe in order to establish the reconstruction method. We obtain explicit forms of $f(Q)$ that can explain the observed accelerated expansion of the Universe without the need for an additional dark energy component by taking into account appropriate cosmological assumptions. Moreover, the reconstructed model can also be extended to the infinite past to model the early universe for certain scenarios. In an FLRW spacetime we have considered a constant deceleration parameter and a constant jerk parameter to facilitate our reconstruction analysis. We further discuss the, general relativity limit, Friedmann consistency and background physical viability of the reconstructed models. The analysis indicates that Raychaudhuri equation, interpreted as an equation governing the focusing/defocusing of cosmological geodesic congruences, can be used as the central equation in an inverse reconstruction of $f(Q)$ gravity.
