Effective equations in quantum cosmology

We develop a general framework for effective equations of expectation value s in quantum cosmology and pose for them the quantum Cauchy problem with no -boundary and tunneling wavefunctions. Cosmological configuration space is decomposed into two sectors that give qualitatively different contributions to the radiation currents in effective equations. The field-theoretical se ctor of inhomogeneous modes is treated by the method of Euclidean effective action, while the quantum mechanical sector of the spatially homogeneous i nflaton is handled by the technique of manifest quantum reduction to gauge invariant cosmological perturbations. We apply this framework in the model with a big negative non-minimal coupling, which incorporates a recently pro posed low energy (GUT scale) mechanism of the quantum origin of the inflati onary Universe and study the effects of the quantum inflaton mode. (C) 2001 Elsevier Science B.V. All rights reserved.