Slow-roll approximation in loop quantum cosmology

TL;DR

This paper develops a systematic slow-roll expansion method within loop quantum cosmology, up to fourth order, to analyze inflationary dynamics and identify potential quantum gravitational effects in cosmological data.

Contribution

It introduces a detailed construction of the slow-roll expansion in loop quantum cosmology, extending previous approaches to higher order and verifying accuracy against numerical solutions.

Findings

Higher-order slow-roll expansion improves approximation accuracy.

Comparison with numerical trajectories validates the method.

Potential to detect quantum gravity effects in cosmological observations.

Abstract

The slow-roll approximation is an analytical approach to study dynamical properties of the inflationary universe. In this article, systematic construction of the slow-roll expansion for effective loop quantum cosmology is presented. The analysis is performed up to the fourth order in both slow-roll parameters and the parameter controlling the strength of deviation from the classical case. The expansion is performed for three types of the slow-roll parameters: Hubble slow-roll parameters, Hubble flow parameters and potential slow-roll parameters. An accuracy of the approximation is verified by comparison with the numerical phase space trajectories for the case with a massive potential term. The results obtained in this article may be helpful in the search for the subtle quantum gravitational effects with use of the cosmological data.