We have investigated the five-dimensional Bianchi type-III string cosmological models with dark energy using the Saez–Ballester scalar-tensor theory of gravitation. To solve the field equations, we applied the laws of volumetric expansions and assumed a scaling relation between the shear scalar \(\sigma \) and the expansion scalar \(\theta \), which leads to a relationship between the metric potentials, i.e., \( D=C^{r} \) (where r is a non-zero constant). We have considered both power-law model and exponential model and have discussed the physical and kinematical parameters of these models.

中文翻译：

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Saez-Ballester 引力标量张量理论中具有暗能量的高维比安奇 III 型弦宇宙学模型

我们利用 Saez-Ballester 标量张量引力理论研究了具有暗能量的五维比安奇 III 型弦宇宙学模型。为了求解场方程，我们应用体积膨胀定律并假设剪切标量\(\sigma \)和膨胀标量\(\theta \)之间的比例关系，这导致了度量势之间的关系，即, \( D=C^{r} \)（其中r是非零常数）。我们考虑了幂律模型和指数模型，并讨论了这些模型的物理和运动学参数。