Quantum reduced loop gravity: extension to scalar field

TL;DR

This paper extends Quantum Reduced Loop Gravity to include scalar fields, providing a regularized Hamiltonian operator with analytic matrix elements, enabling analysis of quantum gravity effects in cosmology.

Contribution

It introduces a scalar field quantization within Quantum Reduced Loop Gravity, using regularization techniques from full Loop Quantum Gravity and deriving analytic matrix elements.

Findings

Regularized Hamiltonian operator for scalar fields derived

Analytic matrix elements obtained for basis states

Enables study of quantum gravity effects in cosmological models

Abstract

The quantization of the Hamiltonian for a scalar field is performed in the framework of Quantum Reduced Loop Gravity. We outline how the regularization can be performed by using the analogous tools adopted in full Loop Quantum Gravity and the matrix elements of the resulting operator between basis states are analytic coefficients. These achievements open the way for a consistent analysis of the Quantum Gravity corrections to the classical dynamics of gravity in the presence of a scalar field in a cosmological setting.