Quantum cosmology in scalar-tensor theories with non-minimal coupling

Quantization in the minisuperspace of non-minimal scalar-tensor theories le ads to a partial differential equation which is non separable. Through a co nformal transformation we can recast the Wheeler-DeWitt equation in an inte grable form, which corresponds to the minimal coupling case, whose general solution is known. Performing the inverse conformal transformation in the s olution thus found, we can construct the corresponding solution in the orig inal frame. This procedure can also be employed with the Bohmian trajectori es. In this way, we can study the classical limit of some particular soluti ons of this quantum model. While the classical limit of these solutions occ urs for small scale factors in the Einstein frame, it happens for small val ues of the scalar field non-minimally coupled to gravity in the Jordan fram e, which includes large scale factors.