Scalar and tensor perturbations in loop quantum cosmology: High-order corrections

TL;DR

This paper derives highly accurate predictions for scalar and tensor perturbations in loop quantum cosmology, incorporating quantum corrections, and constrains their observational effects using current cosmological data.

Contribution

It provides the most precise calculations of inflationary observables in LQC with quantum corrections, including third-order uniform asymptotic approximations.

Findings

Quantum corrections cause deviations in spectra at large scales.

Results are consistent with current observational bounds.

Potential detectability of quantum effects in future experiments.

Abstract

Loop quantum cosmology (LQC) provides promising resolutions to the trans-Planckian issue and initial singularity arising in the inflationary models of general relativity. In general, due to different quantization approaches, LQC involves two types of quantum corrections, the holonomy and inverse-volume, to both of the cosmological background evolution and perturbations. In this paper, using {\em the third-order uniform asymptotic approximations}, we derive explicitly the observational quantities of the slow-roll inflation in the framework of LQC with these quantum corrections. We calculate the power spectra, spectral indices, and running of the spectral indices for both scalar and tensor perturbations, whereby the tensor-to-scalar ratio is obtained. We expand all the observables at the time when the inflationary mode crosses the Hubble horizon. As the upper error bounds for the uniform asymptotic approximation at the third-order are $\lesssim 0.15\%$, these results represent the most accurate results obtained so far in the literature. It is also shown that with the inverse-volume corrections, both scalar and tensor spectra exhibit a deviation from the usual shape at large scales. Then, using the Planck, BAO and SN data we obtain new constraints on quantum gravitational effects from LQC corrections, and find that such effects could be within the detection of the forthcoming experiments.