Recent research finding indicates that the present universe is experiencing an accelerating expansion. Since the general theory of relativity is not sufficient to justify gravity interactions, other theories are required to address these issues. Motivation by this, in this communication, we have decided to study various aspects of the universe within the framework of \(f\left(T \right){}\) modified gravity theory, under the viable assumption that \(V = \sin \left({\beta t} \right)\) , associated with spatial homogeneous and anisotropic Bianchi type-I space–time.