Higher dimensional Bianchi type-III string cosmological models with dark energy in Saez–Ballester scalar-tensor theory of gravitation

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.