Extension of loop quantum gravity to $f(R)$ theories

TL;DR

This paper extends loop quantum gravity to include $f(R)$ theories, demonstrating that the non-perturbative quantization approach is applicable beyond general relativity to a broader class of 4D metric theories.

Contribution

It develops a connection-dynamical formalism for $f(R)$ theories and extends loop quantization to these theories, showing the method's broader validity.

Findings

Loop quantum gravity formalism applied to $f(R)$ theories.

Quantization scheme valid for a wide class of 4D metric theories.

Supports non-perturbative quantization beyond general relativity.

Abstract

The 4-dimensional metric $f(\R)$ theories of gravity are cast into connection-dynamical formalism with real $\SU(2)$-connections as configuration variables. Through this formalism, the classical metric $f(\R)$ theories are quantized by extending the loop quantization scheme of general relativity. Our results imply that the non-perturbative quantization procedure of loop quantum gravity is valid not only for general relativity but also for a rather general class of 4-dimensional metric theories of gravity.