Anomaly freedom in effective Loop Quantum Cosmology refined: extended functional dependence of the counter-terms

TL;DR

This paper explores how counter-terms in effective Loop Quantum Cosmology depend on full phase-space variables, deriving anomalies and imposing new restrictions on holonomy corrections to ensure anomaly freedom.

Contribution

It extends the analysis of counter-terms dependence in Loop Quantum Cosmology to full phase-space variables, providing new restrictions on holonomy corrections.

Findings

Derived anomalies for phase-space dependent counter-terms

Solved the system in specific cases to ensure anomaly freedom

Established new restrictions on generalized holonomy corrections

Abstract

Instead of assuming that they depend only on the background variables, we investigate the hypothesis that counter-terms appearing in the deformed algebra approach to loop quantum cosmology depend on the full phase-space variables. We derive the associated anomalies and solve the entire system in several specific cases. New restrictions on the generalized holonomy corrections are obtained.