Deparametrization and quantization of scalar-tensor gravity and its cosmological model

TL;DR

This paper employs the scalar field in scalar-tensor gravity as a 'time' parameter to deparametrize and nonperturbatively quantize the theory using loop quantum gravity, revealing a quantum bounce replacing the classical big bang singularity.

Contribution

It introduces a novel deparametrization method using the scalar field as time and applies loop quantum gravity to quantize scalar-tensor cosmology.

Findings

Quantum evolution is discrete in the scalar-tensor model.

The classical big bang singularity is replaced by a quantum bounce.

Physical solutions to the quantum Hamiltonian are explicitly obtained.

Abstract

The degree of freedom of the scalar field in scalar-tensor gravity is employed as "time" to deparametrize the Hamiltonian constraint of the theory. The deparametrized system is then nonperturbatively quantized by the approach of loop quantum gravity. This results in a discrete time evolution of the physical states with respect to the gravitational degree of freedom in the quantum theory. In the corresponding Brans-Dicke cosmological model, the physical solutions to the quantum Hamiltonian constraint are obtained in the light of the deparametrization. The quantum dynamics indicates that the classical big bang singularity is replaced by a quantum bounce.