WHEELER-DEWITT EQUATIONS FOR 4TH-ORDER QUANTUM COSMOLOGY

We compare the methods proposed by Boulware, and Buchbinder and Lyacho vich, to establish a Hamiltonian formalism for fourth-order gravity an d study another possibility to circumvent second-order derivatives of the metric tensor components on the level of the Lagrangian for fourth -order theories of gravity, by introduction of a scalar field. This is done in a way different from the common procedure of doing a conforma l transformation of the metric. It is demonstrated how the well known fourth-order field equations result. On the basis of the Hamiltonian f ormalism, we consider the quantum cosmology for homogeneous and isotro pic closed models. As a first application, the WKB approximation is di scussed neglecting the spatial curvature. Chosen initial conditions ha ve the consequence that the resulting wavefunction leads to the inflat ionary stage of the cosmic evolution.