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.
