Consistency of holonomy-corrected scalar, vector and tensor perturbations in Loop Quantum Cosmology

Abstract

Loop Quantum Cosmology yields two kinds of quantum corrections to the effective equations of motion for cosmological perturbations. Here we focus on the holonomy kind and we study the problem of the closure of the resulting algebra of constraints. Up to now, tensor, vector and scalar perturbations were studied independently, leading to different algebras of constraints. The structures of the related algebras were imposed by the requirement of anomaly freedom. In this article we show that the algebra can be modified by a very simple quantum correction, holding for all types of perturbations. This demonstrates the consistency of the theory and shows that lessons from the study of scalar perturbations should be taken into account when studying tensor modes. The Mukhanov-Sasaki equations of motion are similarly modified by a simple term.

5 pages

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• Non-singular bounce scenarios in loop quantum cosmology and the effective field description
• Anomaly-free cosmological perturbations in effective canonical quantum gravity
• A $\Lambda$CDM bounce scenario
• Bounce universe from string-inspired Gauss-Bonnet gravity
• A quantitative analysis of singular inflation with scalar-tensor and modified gravity
• $\Lambda$CDM Bounce Cosmology without $\Lambda$CDM: the case of modified gravity
• Gravitational quantum effects on power spectra and spectral indices with higher-order corrections
• Uniqueness of the Fock quantization of scalar fields and processes with signature change in cosmology
• Viability of the Matter Bounce Scenario
• Report on the session QG4 of the 13th Marcel Grossmann Meeting