Loop quantum modified gravity and its cosmological application

TL;DR

This paper reviews a nonperturbative loop quantum gravity approach for metric modified theories, specifically applying it to scalar-tensor theories and developing a quantum cosmology framework with effective dynamical equations.

Contribution

It introduces a rigorous loop quantum gravity quantization method for scalar-tensor theories and constructs the foundational structure for loop quantum Brans-Dicke cosmology.

Findings

Well-defined Hamiltonian and master constraint operators

Established a quantum kinematical framework for scalar-tensor theories

Derived effective dynamical equations for loop quantum Brans-Dicke cosmology

Abstract

A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously constructed. Both the Hamiltonian and master constraint operators are well defined and proposed to represent quantum dynamics of scalar-tensor theories. As an application to models, we set up the basic structure of loop quantum Brans-Dicke cosmology. The effective dynamical equations of loop quantum Brans-Dicke cosmology are also obtained, which lay a foundation for the phenomenological investigation to possible quantum gravity effects in cosmology.