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Abstract The paper deals with cosmological solutions describing different phases of the Universe for the homogeneous and isotropic FLRW model of the Universe with torsion. Normally, torsion field is not suitable for maximally symmetric space time model. However, one may use a specific profile of vectorial torsion field, derived from a scalar function. By proper choices of the torsion scalar function, it is shown that a continuous cosmic evolution starting from the emergent scenario to the present late time acceleration is possible. Also thermodynamics of the system is analyzed and equivalence with Einstein gravity is discussed.