Comparison of primordial tensor power spectra from the deformed algebra and dressed metric approaches in loop quantum cosmology

TL;DR

This paper compares two approaches in loop quantum cosmology for predicting primordial tensor power spectra, revealing similarities at large scales and significant differences at small scales, with potential observational implications.

Contribution

It provides a detailed comparison of the dressed metric and deformed algebra approaches, including analytical and numerical calculations of their tensor power spectra.

Findings

Large scale behaviors are similar and compatible with general relativity.

Small scale behaviors differ drastically between approaches.

Both approaches agree on predictions that differ from classical GR and are parameter-independent.

Abstract

Loop quantum cosmology tries to capture the main ideas of loop quantum gravity and to apply them to the Universe as a whole. Two main approaches within this framework have been considered to date for the study of cosmological perturbations: the dressed metric approach and the deformed algebra approach. They both have advantages and drawbacks. In this article, we accurately compare their predictions. In particular, we compute the associated primordial tensor power spectra. We show -- numerically and analytically -- that the large scale behavior is similar for both approaches and compatible with the usual prediction of general relativity. The small scale behavior is, the other way round, drastically different. Most importantly, we show that in a range of wavenumbers explicitly calculated, both approaches do agree on predictions that, in addition, differ from standard general relativity and do not depend on unknown parameters. These features of the power spectrum at intermediate scales might constitute a universal loop quantum cosmology prediction that can hopefully lead to observational tests and constraints. We also present a complete analytical study of the background evolution for the bouncing universe that can be used for other purposes.