Can the diffeomorphism and Gauss constraints be holonomy corrected in the deformed algebra approach to modified gravity?

2025/10/27 by Thézier, Jamy-Jayme, Barrau, Aurélien, Martineau, Killian +1
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc)

paper · doi:10.48550/arxiv.2510.23194

Abstract

Deforming the algebra of constraint is a well known approach to effective loop quantum cosmology. More generally, it is a consistent way to modify gravity from the Hamiltonian perspective. In this framework, the Hamiltonian (scalar) constraint is usually the only one to be holonomy corrected. As a heuristic hypothesis, we consider the possibility to also correct the diffeomorphism and Gauss constraints. It is shown that it is impossible to correct the diffeomorphism constraint without correcting the Gauss one, while maintaining a first-class algebra. However, if all constraints are corrected, the algebra can be closed. The resulting differential equations to be fulfilled by the corrections (of the background and of the perturbations) are derived.

Citations

• Anomaly freedom in effective Loop Quantum Cosmology refined: extended functional dependence of the counter-terms
• Anomaly freedom in effective Loop Quantum Cosmology: pedagogical summary and generalized holonomy corrections
• A new look at scalar perturbations in loop quantum cosmology: (un)deformed algebra approach using self dual variables
• Cosmology without time: What to do with a possible signature change from quantum gravitational origin?

Related

• Discretisations, Constraints and Diffeomorphisms in Quantum Gravity
• A new look at scalar perturbations in loop quantum cosmology: (un)deformed algebra approach using self dual variables
• Constraint Analysis of Linearized Gravity and a Generalization of the HTZ Approach
• Diffeomorphism symmetry in quantum gravity models
• Hamiltonian consistency of the gravitational constraint algebra under deformations