Deparametrization and quantization of scalar-tensor gravity and its cosmological model

The degree of freedom of the scalar field in scalar-tensor gravity is employed as "time" to deparametrize the Hamiltonian constraint of the theory. The deparametrized system is then nonperturbatively quantized by the approach of loop quantum gravity. This results in a discrete time evolution of the physical states with respect to the gravitational degree of freedom in the quantum theory. In the corresponding Brans-Dicke cosmological model, the physical solutions to the quantum Hamiltonian constraint are obtained in the light of the deparametrization. The quantum dynamics indicates that the classical big bang singularity is replaced by a quantum bounce.