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

Abstract

The 4-dimensional metric $f(\mathbb{R})$ theories of gravity are cast into connection-dynamical formalism with real $\SU(2)$-connections as configuration variables. Through this formalism, the classical metric $f(\mathbb{R})$ 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.

4 pages;Revised version adapted for PRL

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