  While loop quantum cosmology (LQC) predicts a robust quantum bounce of the
background evolution of a Friedmann-Robertson-Walker (FRW) spacetime prior to
the standard slow-roll inflation, whereby the big bang singularity is resolved,
there are several different quantization procedures to cosmological
perturbations, for instance, {\em the deformed algebra, dressed metric, and
hybrid quantizations}. This paper devotes to study the quantum bounce effects
of primordial perturbations in the hybrid approach. The main discrepancy of
this approach is the effective positive mass at the quantum bounce for the
evolution of the background that is dominated by the kinetic energy of the
inflaton field at the bounce, while this mass is always nonpositive in the
dressed metric approach. It is this positivity of the effective mass that
violates the adiabatic evolution of primordial perturbations at the initial
moments of the quantum bounce. With the assumption that the evolution of the
background is dominated by the kinetic energy of the inflaton at the bounce, we
find that the effective potentials for both scalar and tensor perturbations can
be well approximately described by a P\"{o}schl-Teller (PT) potential, which
allows us to find analytical solutions of perturbations, and from these
analytical expressions we are able to study the non-adiabatic evolution of
primordial perturbations in details. In particular, we derive their quantum
bounce effects and investigate their observational constraints. In addition,
the impacts of quantum bounce effects on the non-Gaussinity and their
implication on the explanations of observed power asymmetry in CMB have also
been explored.
