标题： 测地线偏离在Saez-Ballester理论中 显示英文标题

标题： Geodesic deviation in Saez--Ballester theory

摘要： 我们研究了广义版本的Sáez--Ballester(SB)理论中的测地线偏离(GD)方程，在任意维度中进行研究。我们首先建立了一个通用的形式，然后限制到特定情况，其中(i)物质-能量分布为完美流体，(ii)时空几何由零Weyl张量描述。此外，我们将空间平坦的FLRW宇宙作为背景几何。基于此设置，我们计算了与基本观测者和过去指向的零向量场相关的GD方程以及收敛条件。此外，我们扩展了该框架，并在\emph{修改的}Sáez--Ballester理论(MSBT)中提取了相应的测地线偏离，其中能量-动量张量和势严格来源于额外维度的几何结构。为了检验本文中的GD方程，我们在SB框架内考虑了两个新颖的宇宙学模型。此外，我们在所述的SB和MSBT框架内讨论了一些本质模型和合适的幻影暗能量情景。注意到我们在此处的宇宙学模型可以适当包含我们宇宙的当前时期，我们解析和/或数值地求解了GD方程。通过使用正确的能量条件以及最近的观测数据，我们一致地描绘了偏差矢量$\eta(z)$和观测者面积距离$r_0(z)$对于我们的模型的行为。关于哈勃常数问题，我们特别关注由Planck合作组和SH0ES合作组报告的观测数据，以描绘我们此处的幻影模型中的$\eta(z)$和$r_0(z)$。随后，我们将我们的结果与与$\Lambda$CDM模型相关的结果进行对比。 显示英文摘要

摘要： We study the geodesic deviation (GD) equation in a generalized version of the S\'{a}ez--Ballester (SB) theory in arbitrary dimensions. We first establish a general formalism and then restrict to particular cases, where (i) the matter-energy distribution is that of a perfect fluid, and (ii) the spacetime geometry is described by a vanishing Weyl tensor. Furthermore, we consider the spatially flat FLRW universe as the background geometry. Based on this setup, we compute the GD equation as well as the convergence condition associated with fundamental observers and past directed null vector fields. Moreover, we extend that framework and extract the corresponding geodesic deviation in the \emph{modified} S\'{a}ez--Ballester theory (MSBT), where the energy-momentum tensor and potential emerge strictly from the geometry of the extra dimensions. In order to examine our herein GD equations, we consider two novel cosmological models within the SB framework. Moreover, we discuss a few quintessential models and a suitable phantom dark energy scenario within the mentioned SB and MSBT frameworks. Noticing that our herein cosmological models can suitably include the present time of our Universe, we solve the GD equations analytically and/or numerically. By employing the correct energy conditions plus recent observational data, we consistently depict the behavior of the deviation vector $\eta(z)$ and the observer area distance $r_0(z)$ for our models. Concerning the Hubble constant problem, we specifically focus on the observational data reported by the Planck collaboration and the SH0ES collaboration to depict $\eta(z)$ and $r_0(z)$ for our herein phantom model. Subsequently, we contrast our results with those associated with the $\Lambda$CDM model.