Loop quantum $f(R)$ theories

TL;DR

This paper extends the loop quantum gravity formalism to 4-dimensional metric $f(R)$ theories, enabling non-perturbative quantization of these modified gravity models.

Contribution

It develops a connection dynamical formalism for $f(R)$ theories and constructs the quantum kinematical framework, including well-defined Hamiltonian and master constraint operators.

Findings

Quantum kinematical framework for $f(R)$ gravity is rigorously constructed.

Hamiltonian and master constraint operators are well defined for $f(R)$ theories.

Loop quantum gravity quantization applies to a broad class of 4D metric theories.

Abstract

As modified gravity theories, the 4-dimensional metric $f(R)$ theories are cast into connection dynamical formalism with real $su(2)$-connections as configuration variables. This formalism enables us to extend the non-perturbative loop quantization scheme of general relativity to any metric $f(R)$ theories. The quantum kinematical framework of $f(R)$ gravity is rigorously constructed, where the quantum dynamics can be launched. Both Hamiltonian constraint operator and master constraint operator for $f(R)$ theories are well defined. Our results show that the non-perturbative quantization procedure of loop quantum gravity are valid not only for general relativity but also for a rather general class of 4-dimensional metric theories of gravity.