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

Non-adiabatic Evolution of Primordial Perturbations and non-Gaussinity in Hybrid Approach of Loop Quantum Cosmology