Quantisation ambiguities and the effective dynamics of scalar-tensor theories in loop quantum cosmology

The Hamiltonian constraint of scalar-tensor theories in the Jordan frame is quantised using three quantisation prescriptions in loop quantum cosmology, from which we obtain three different effective Hamiltonian constraints. The corresponding effective equations of motion derived from these effective Hamiltonian constraints turn out to be drastically different. The implications of each set of effective equations of motion are discussed in detail. In the latter half of this paper, as a concrete example, we study the effective dynamics of a specific model with the non-minimal coupling function $F(\phi)=1+\xi\kappa\phi^2$ and self-interacting quartic potential. Using numerical results, we find different features for different effective dynamics. Moreover, it is also found that the spacetime singularity is absent and the cosmological bounce exists in each effective dynamics of this model.