Extension of loop quantum gravity to $f(R)$ theories
  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. 
Xiangdong Zhang and Yongge Ma
gr-qc astro-ph.CO hep-th math-ph math.MP quant-ph