While loop quantum cosmology predicts a robust quantum bounce of the background evolution of a Friedmann-Robertson-Walker 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, the deformed algebra, dressed metric, and hybrid quantizations. This paper is devoted to studying 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 Pöschl-Teller potential, which allows us to find analytical solutions of perturbations, and from these analytical expressions we are able to study the nonadiabatic evolution of primordial perturbations in detail. In particular, we derive their quantum bounce effects and investigate their observational constraints. In addition, the impacts of quantum bounce effects on the non-Gaussianity and their implication on the explanations of the observed power asymmetry in the cosmic microwave background are also explored.

• Received 17 September 2018

DOI:https://doi.org/10.1103/PhysRevD.98.103528