  We study the cosmological effect of the simple scalar-torsion ($0^+$) 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 $\rho_T$
has a radiation-like asymptotic behavior of $a^{-4}$ with $a$ representing the
scale factor, along with the stable point of the torsion pressure ($P_T$) and
density ratio $P_T/\rho_T\rightarrow 1/3$ 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.
