Primordial non-Gaussianity and power asymmetry with quantum gravitational effects in loop quantum cosmology

Loop quantum cosmology (LQC) provides a resolution of the classical big bang singularity in the deep Planck era. The evolution, prior to the usual slow-roll inflation, naturally generates excited states at the onset of the slow-roll inflation. It is expected that these quantum gravitational effects could leave its fingerprints on the primordial perturbation spectrum and non-Gaussianity, and lead to some observational evidences in the cosmic microwave background (CMB). While the impact of the quantum effects on the primordial perturbation spectrum has been already studied and constrained by current data, in this paper we continue studying such effects on the non-Gaussianity of the primordial curvature perturbations. In this paper, we present detailed and analytical calculations of the non-Gaussianity and show explicitly that the corrections due to quantum effects are in the same magnitude of the slow-roll parameters in the observable scales and thus are well within current observational constraints. Despite this, we show that the non-Gaussianity in the squeezed limit can be enhanced at superhorizon scales and further, these effects may yield a large statistical anisotropy on the power spectrum through the Erickcek-Kamionkowski-Carroll mechanism.