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We study the cosmological effect of the simple scalar-torsion () mode in Poincar'{e} gauge theory of gravity. We find that for the non-constant (affine) curvature case, the early evolution of the torsion density has a radiation-like asymptotic behavior of with representing the scale factor, along with the stable point of the torsion pressure () and density ratio in the high redshift regime $(z \gg 0)$, which is different from the previous result in the literature. We use the Laurent expansion to resolve the solution. We also illustrate our result by the execution of numerical computations.

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