Cosmic evolution of Kantowski-Sachs universe in the context of bulk viscous string in teleparallel gravity

In the present work, we have analysed the Kantowski-Sachs cosmological model with teleparallel gravity, where a bulk viscous fluid containing one-dimensional cosmic strings serves as the source for the energy-momentum tensor. To obtain the deterministic solution of the field equations, we employed the proportionality condition linking the shear scalar ({σ}) and the expansion scalar ({θ}), which establishes a relationship between metric potentials. Another approach employed was the utilisation of the Hybrid Expansion Law (HEL). The discussion focuses on the behaviour of the accelerating universe concerning the specific choice of a highly non-linear form of teleparallel gravity f(T) = {α}T + {eta}T m, where T is the torsion scalar, {α}, {eta} are model parameter and m is a positive integer. The equation of state parameter ({ω}) in this model supports the acceleration behaviour of the universe. We observed that the null energy condition and weak energy condition are obeyed while violating the strong energy condition as per the present accelerating expansion. It has been observed that, under specific model parameter constraints, the universe transitions from a decelerating to an accelerated phase.