We study cosmological consequences of the dark spinor model when torsion is included. Only some components of the torsion are allowed to be non-vanishing in homogeneous and isotropic cosmology, but there exist freedoms in the choice of these components which is consistent with the evolution equations. We exploit this and discuss several cases which can result in interesting cosmological consequences. Especially, we show that there exist exact cosmological solutions in which the Universe began its acceleration only recently and this solution is an attractor. This corresponds to a specific form of the torsion with a mild fine-tuning which can address the coincidence problem.
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