Dressed metric predictions revisited

TL;DR

This paper critically examines the dressed metric approach in loop quantum cosmology, revealing that many predictions rely on ill-defined quantities and proposing a new, well-defined scheme to improve the reliability of pre-inflationary physics predictions.

Contribution

It identifies fundamental issues in the dressed metric approach and introduces a new scheme based on well-defined quantities for more accurate cosmological predictions.

Findings

Most steps in the dressed metric predictions are ill-defined.

Previous models' agreement with data is explained by reliance on ill-defined quantities.

A new scheme with well-defined quantities is proposed.

Abstract

It was recently shown that the volume operator of loop quantum cosmology (LQC) and all its positive powers are ill-defined on physical states. In this paper, we investigate how it effects predictions of cosmic microwave background (CMB) power spectra obtained within dressed metric approach for which expectations values of $\hat{a}$ are the key element. We find that almost every step in the procedure is ill-defined and relies heavily upon a (seemingly premature) numerical truncation. Thus, it suggests that more care is needed in making predictions regarding pre-inflationary physics. We propose a new scheme which contains only well-defined quantities. The surprising agreement of the hitherto models with observational data, especially at low angular momenta $l$ is explained.