Abstract
We consider a cosmological model in which a scalar field is non-minimally coupled to scalar torsion and a vector field through two coupling functions in the framework of teleparallel gravity. The explicit forms of the coupling functions and the scalar field potential are explored, under the assumption that the Lagrangian admits the Noether symmetry in the Friedmann–Lemaitre–Robertson–Walker (FLRW) space–time. The existence of such symmetry allows to solve the equations of motion and achieve exact solutions of the scale factor, scalar and vector fields. It is found that the vector field contributes significantly in the accelerating expansion of the universe in the early times, while the scalar field plays an essential role in the late times.
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