  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 Hamiltonian and master constraint operators
are well defined 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.
