  In this letter, we study the late-time evolution of a torsion cosmology only
with the spin-$0^+$ mode. We find three kinds of analytical solutions with a
constant affine scalar curvature. In the first case, it is not physical because
the matter density will be negative. In the second case, it shows that the dark
energy can be mimicked in the torsion cosmological model. In the third case,
the characteristic of late-time evolution is similar to that of the universe of
matter dominant. And we also find a kind of expression with the non-constant
curvature that the periodic character of numerical calculation is only the
reflection of solution in a specific period of evolution. Using these
expressions, we shall be able to predict the evolution over the late-time. From
this prediction, we know the fate of universe that the universe would expand
forever, slowly asymtotically to a halt.
