中文摘要：

A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously constructed. Both the Hanfiltonian and master constraint operators are well defned and proposed to represent quantum dynamics of scalar-tensor theories. As an application to models, we set up the basic structure of loop quantum Brans Dicke cosmology. The effective dynamical equations of loop quantum Brans Dicke cosmology are also obtained, which lay a foundation for the phenomenological investigation to possible quantum gravity effects in cosmology.