Anomaly-free scalar perturbations with holonomy corrections in loop quantum cosmology

TL;DR

This paper investigates holonomy corrections to scalar perturbations in loop quantum cosmology, introduces counter-terms to ensure anomaly freedom, and derives equations of motion with potential cosmological implications.

Contribution

It provides explicit conditions and expressions for counter-terms to achieve anomaly-free scalar perturbations in loop quantum cosmology, revealing a natural emergence of a new quantization scheme.

Findings

Explicit anomaly-free conditions and counter-terms derived.

Gauge-invariant variables and equations of motion established.

Qualitative discussion of cosmological consequences included.

Abstract

Holonomy corrections to scalar perturbations are investigated in the loop quantum cosmology framework. Due to the effective approach, modifications of the algebra of constraints generically lead to anomalies. In order to remove those anomalies, counter-terms are introduced. We find a way to explicitly fulfill the conditions for anomaly freedom and we give explicit expressions for the counter-terms. Surprisingly, the "new quantization scheme" naturally arises in this procedure. The gauge invariant variables are found and equations of motion for the anomaly-free scalar perturbations are derived. Finally, some cosmological consequences are discussed qualitatively.