Some Bianchi Type Viscous Holographic Dark Energy Cosmological Models in the Brans–Dicke Theory

In this article, we analyze Bianchi type–II, VIII, and IX spatially homogeneous and anisotropic space-times in the background of the Brans–Dicke theory of gravity within the framework of viscous holographic dark energy. To solve the field equations, we have used the relation between the metric potentials as $R=S^n$ and the relation between the scalar field $\varphi$ and the scale factor $a$ as $\varphi =a^m$ . Also, we have discussed some of the dynamical parameters of the obtained models, such as the deceleration parameter $\left(q\right)$ , the jerk parameter $\left(\hspace{0.17em}j\right)$ , the EoS parameter $\left({\omega }_{vhde}\right)$ , the density parameter $\left({\Omega }_{\text{vhde}}\right)$ , Om-diagnostic, squared speed of sound $\left(v_s^2\right)$ , EoS plane $\left({\omega }_{vhde}-{\omega }_{vhde}^{\prime }\right)$ , and statefinder plane $\left(r\hspace{0.17em}-\hspace{0.17em}s\right)$ through graphical representation, which are significant in the discussion of cosmology. Furthermore, all the models obtained and graphically presented shown an expanding and accelerating Universe, which is in better agreement with the latest experimental data. The viscous holographic dark energy models are compatible with explaining the present cosmic accelerated expansion.