  In previous work, we showed that in loop quantum cosmology of scalar-tensor
theory (STT) with the holonomy correction the background equations of motion in
the Jordan frame have two branches, i.e., the $b_{+}$ branch and the $b_{-}$
branch. In the low-energy limit, the $b_{+}$ branch of the equations of motion
reproduce the equations of motion of classical STT while the $b_{-}$ branch of
equations of motion do not reproduce the classical equations. In this paper, we
investigate cosmological dynamics in an expanding universe whose background is
described by the the $b_{-}$ branch of equations of motion of STT, and we
especially focus on the dynamics of the perturbations in the low-energy limit
because it is most relevant to the current observational range. First, we find
a low-energy effective Hamiltonian which can yield the low-energy limit of the
$b_{-}$ branch of equations, this Hamiltonian consists of constraints whose
constraint algebra is different from the classical case but also closed up to
arbitrary order of perturbations. Remarkably, we find that this Hamiltonian can
be transformed into the Hamiltonian of the Einstein frame by field
redefinitions. Moreover, we also develop the linear cosmological perturbation
theory and apply it to study the slow-roll inflation. Finally, we study a
specific model of STT. In this model, a contracting universe described by
classical STT in the remote past can pass through the bounce and evolve into an
expanding universe whose background dynamics is described by the $b_{-}$ branch
of equations of motion. It is shown that the slow-roll inflation can take place
in this case, and the spectral indices of the slow-roll inflation agree well
with the observations. The results in this paper indicate that there exists an
alternative consistent theory which is different from the classical theory in
the low-energy limit of loop quantum STT.
