Homogeneous anisotropic cosmological model admitting Noether symmetries in extended teleparallel gravity

In this paper, we intend to explore homogeneous anisotropic cosmological model via Noether symmetry approach in the modified teleparallel f(T) gravity, where f(T) is a function of the torsion scalar T. Primarily, we formulate equations of motion considering a general form of the aforementioned cosmological model in the f(T) gravity. The formulated equations being highly nonlinear and do not admit closed form analytical solution. We adopt Bianchi type VIII and IX geometries as particular examples of such spatially homogeneous anisotropic cosmological model. Moreover, in order to solve the resulting equations, we consider both linear as well as a quadratic function of the torsion scalar T. Together with such forms of f(T) gravity, we adopt a power law relation between the scale factors in order to explore cosmologically viable model. We further use these solutions to calculate first integral of motion. We also explore the dynamics of the obtained cosmological models via the Hubble parameter, deceleration parameter and shear scalar. We observe a smooth oscillatory evolution of the obtained models around a well-defined equilibrium values which indicate a stable geometrical structure. Moreover, the torsion scalar follows a regular periodic pattern which seems to be consistent with the oscillatory nature of the scale factors.