Non-Gaussian features from the inverse volume corrections in loop quantum cosmology

Abstract

In this paper we study the non-Gaussian features of the primordial fluctuations in loop quantum cosmology with the inverse volume corrections. The detailed analysis is performed in the single field slow-roll inflationary models. However, our results reflect the universal characteristics of bispectrum in loop quantum cosmology. The main corrections to the scalar bispectrum come from two aspects: one is the modifications to the standard Bunch--Davies vacuum, and the other is the corrections to the background dependent variables, such as slow-roll parameters. Our calculations show that the loop quantum corrections make ${f}_{\mathrm{NL}}$ of the inflationary models increase 0.1%. Moreover, we find that two new shapes of non-Gaussian signal arise, which we name ${\mathcal{F}}_{1}$ and ${\mathcal{F}}_{2}$. The former gives a unique loop quantum feature, which is less correlated with the local, equilateral, and single types, while the latter is highly correlated with the local one.