Wheeler-De Witt equations for fourth-order quantum cosmology

Abstract

The author compares the methods proposed by Boulware (1984), and Buchbinder and Lyachovich (1987), to establish a Hamiltonian formalism for fourth-order gravity and studies 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 conformal transformation of the metric. It is demonstrated how the well known fourth-order field equations result. On the basis of the Hamiltonian formalism, the author considers the quantum cosmology for homogeneous and isotropic closed models. As a first application, the WKB approximation is discussed neglecting the spatial curvature. Chosen initial conditions have the consequence that the resulting wavefunction leads to the inflationary stage of the cosmic evolution.