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

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

2011-06-19

arxiv.org/abs/1106.3744v2

Class. Quantum Grav. 29 (2012) 085009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, 1 figure. Matches version published in Class. Quantum Grav

Scientific paper

10.1088/0264-9381/29/8/085009

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.

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