Saez-Ballester理论中的测地偏差
Geodesic deviation in Saez--Ballester theory
摘要：
本文研究了任意维Sáez-Ballester（SB）理论的推广形式中的测地线偏差（GD）方程。我们首先建立一个一般的形式主义，然后限制到特定的情况下，（i）的物质能量分布是一个完美的流体，和（ii）时空几何描述的外尔张量消失。此外，我们考虑空间平坦的FLRW宇宙作为背景几何。在此基础上，我们计算了GD方程以及与基本观测器和过去有向零向量场相关的收敛条件。此外，我们扩展了该框架，并提取相应的测地线偏差在\emph{modified} Sáez-Ballester理论（MSBT），其中的能量动量张量和潜力出现严格的几何额外的维度。为了检验我们这里的GD方程，我们考虑了SB框架内的两个新的宇宙学模型。此外，我们讨论了几个典型的模型和一个合适的幻影暗能量的情况下提到的SB和MSBT框架。注意到我们这里的宇宙学模型可以适当地包括我们宇宙的当前时间，我们通过解析和/或数值方法求解了GD方程。通过采用正确的能量条件加上最近的观测数据，我们一致地描述了我们的模型的偏差矢量$η(z)$和观测者区域距离$r_0(z)$的行为。关于哈勃常数的问题，我们特别关注的观测数据报告的普朗克合作和SH 0 ES合作描绘$η(z)$和$r_0(z)$为我们的幻影模型。随后，我们将我们的结果与那些与$Λ$ CDM模型。
英文摘要：
We study the geodesic deviation (GD) equation in a generalized version of the Sáez--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} Sáez--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 $η(z)$ 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 $η(z)$ and $r_0(z)$ for our herein phantom model. Subsequently, we contrast our results with those associated with the $Λ$CDM model.
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