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

TL;DR

This paper demonstrates that a simple quantum correction can unify the algebra of constraints for scalar, vector, and tensor perturbations in Loop Quantum Cosmology, ensuring consistency across all perturbation types.

Contribution

It introduces a straightforward quantum correction that modifies the algebra of constraints uniformly for all perturbation types, enhancing the consistency of Loop Quantum Cosmology.

Findings

Unified algebra for all perturbation types achieved

Modified Mukhanov-Sasaki equations with a simple correction

Demonstrates consistency of holonomy corrections across perturbations

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.