Loop quantum $f(R)$ theories

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