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

TL;DR

This paper explores how vector perturbations in loop quantum cosmology can be made anomaly-free with holonomy corrections, deriving conditions for consistency and analyzing mode propagation through the cosmological bounce.

Contribution

It introduces conditions and counter-terms to ensure anomaly freedom of vector perturbations with holonomy corrections in loop quantum cosmology.

Findings

Conditions for anomaly freedom at all orders

Counter-terms in the Hamiltonian constraint

Propagation of vector modes through the bounce

Abstract

We investigate vector perturbations with holonomy corrections in the framework of loop quantum cosmology. Conditions to achieve anomaly freedom for these perturbations are found at all orders. This requires the introduction of counter-terms in the hamiltonian constraint. We also show that anomaly freedom requires the diffeomorphism constraint to hold its classical form when scalar matter is added although the issue of a vector matter source, required for full consistency, remains to be investigated. The gauge-invariant variable and the corresponding equation of motion are derived. The propagation of vector modes through the bounce is finally discussed.